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Chud Fri 15 Sep 2023 11:58:27 No.151842 View View Original Report

Quoted By: >>151861 >>151862 >>151870 >>151889

darling website

Chud Fri 15 Sep 2023 11:58:57 No.151843 Report

Quoted By: >>151845

Marge, I'm confused.

Chud Fri 15 Sep 2023 11:59:39 No.151844 Report

Margerald

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Chud Fri 15 Sep 2023 11:59:55 No.151845 Report

Quoted By: >>151862

>>151843
darling is sharty culture

Chud Fri 15 Sep 2023 12:01:03 No.151846 Report

Quoted By: >>151847

I don’t get it. What’s darling?

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Chud Fri 15 Sep 2023 12:02:20 No.151847 Report

Quoted By: >>151862

>>151846
my gf

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Chud Fri 15 Sep 2023 12:07:34 No.151848 Report

Quoted By: >>151862

she cute

darling۰۸۴۴.jpg, 1000x1000

Chud Fri 15 Sep 2023 12:08:27 No.151849 Report

Quoted By: >>151862

Chud Fri 15 Sep 2023 12:09:23 No.151850 Report

only trans queens allowed in this thread

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Chud Fri 15 Sep 2023 12:12:26 No.151851 Report

Quoted By: >>151852 >>151853 >>151862

sharty boy meets 'fe girl

Chud Fri 15 Sep 2023 12:13:12 No.151852 Report

>>151851
that's me meeting your mother albeit

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Chud Fri 15 Sep 2023 12:15:33 No.151853 Report

Quoted By: >>151854 >>151862

>>151851
more pics~

darling۱۰۲۴.png, 900x840

Chud Fri 15 Sep 2023 12:18:40 No.151854 Report

Quoted By: >>151855 >>151856 >>151862

>>151853
more

darling۱۰۲۰.jpg, 640x912

Chud Fri 15 Sep 2023 12:19:13 No.151855 Report

Quoted By: >>151862

>>151854
last meeting pic

Chud Fri 15 Sep 2023 12:19:26 No.151856 Report

Quoted By: >>151860

>>151854
this is me with your mother right before i buried my dick in her vagina and then months later a piece of shit offspring, (You) came to be

1660862116674.png, 471x648

Chud Fri 15 Sep 2023 12:19:46 No.151857 Report

Quoted By: >>151862

Chud Fri 15 Sep 2023 12:20:38 No.151858 Report

Quoted By: >>151859

iirc this show was femdombait+the ending sucked

Chud Fri 15 Sep 2023 12:21:30 No.151859 Report

>>151858
read manga + fanmade manga

darling۱۰۱۳.jpg, 850x709

Chud Fri 15 Sep 2023 12:22:10 No.151860 Report

Quoted By: >>151862

>>151856
meds

Chud Fri 15 Sep 2023 12:22:34 No.151861 Report

>>151842
op here im trans if that matters

Chud Fri 15 Sep 2023 12:22:50 No.151862 Report

Quoted By: >>151863

>>151842
>>151845
>>151847
>>151848
>>151849
>>151851
>>151853
>>151854
>>151855
>>151857
>>151860
Im trans btw not sure if that matters

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Chud Fri 15 Sep 2023 12:24:20 No.151863 Report

Quoted By: >>151867

>>151862
meds chuddy

darling۰۹۱۴.png, 946x832, darling۰۹۱۳.jpg, 1400x989, darling۰۹۱۲.png, 600x1560

Chud Fri 15 Sep 2023 12:25:34 No.151864 Report

Quoted By: >>151865

she is kinda abusive tho

Chud Fri 15 Sep 2023 12:27:22 No.151865 Report

>>151864
omgsisa

Chud Fri 15 Sep 2023 12:28:47 No.151866 Report

Quoted By: >>151868

Chud Fri 15 Sep 2023 12:29:18 No.151867 Report

Quoted By: >>151869

>>151863
why are you talking to yourself

Chud Fri 15 Sep 2023 12:29:22 No.151868 Report

>>151866
down

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Chud Fri 15 Sep 2023 12:29:55 No.151869 Report

Quoted By: >>151873

>>151867
that wasn't me

Chud Fri 15 Sep 2023 12:30:02 No.151870 Report

Quoted By: >>151874

>>151842
Thats the cow and chicken red guy thoughbeit

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Chud Fri 15 Sep 2023 12:30:14 No.151871 Report

>yeahhh just gonna let this one stay uppp

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Chud Fri 15 Sep 2023 12:30:20 No.151872 Report

Quoted By: >>151876

Chud Fri 15 Sep 2023 12:30:40 No.151873 Report

Quoted By: >>151875

>>151869
yes it is
Just removed your image perms btw

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Chud Fri 15 Sep 2023 12:30:53 No.151874 Report

>>151870
has 02 hair shooped on him tho

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Chud Fri 15 Sep 2023 12:31:29 No.151875 Report

Quoted By: >>151877

>>151873
esl

Chud Fri 15 Sep 2023 12:31:51 No.151876 Report

>>151872
negated

Chud Fri 15 Sep 2023 12:32:53 No.151877 Report

Quoted By: >>151878 >>151880

>>151875
Banned for ban evasion

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Chud Fri 15 Sep 2023 12:34:00 No.151878 Report

>>151877
??

Chud Fri 15 Sep 2023 12:34:49 No.151879 Report

Quoted By: >>151882

The exponential of this is the orthogonal matrix for rotation around axis v by angle θ; setting c = cos
θ
/
2
, s = sin
θ
/
2
,

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Chud Fri 15 Sep 2023 12:35:08 No.151880 Report

>>151877
meds + bdh(big darling horn)

Chud Fri 15 Sep 2023 12:35:25 No.151881 Report

Quoted By: >>151883

Main menu

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Contents hide
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Transpose of a matrix
Toggle Transpose of a matrix subsection
Definition
Matrix definitions involving transposition
Examples
Properties
Products
Implementation of matrix transposition on computers
Transposes of linear maps and bilinear forms
Toggle Transposes of linear maps and bilinear forms subsection
Transpose of a linear map
Transpose of a bilinear form
Adjoint
See also
References
Further reading
External links
Transpose

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From Wikipedia, the free encyclopedia
This article is about the transpose of matrices and linear operators. For other uses, see Transposition (disambiguation).

The transpose AT of a matrix A can be obtained by reflecting the elements along its main diagonal. Repeating the process on the transposed matrix returns the elements to their original position.
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by AT (among other notations).[1]

The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley.[2] In the case of a logical matrix representing a binary relation R, the transpose corresponds to the converse relation RT.

Transpose of a matrix
Note that this article assumes that matrices are taken over a commutative ring. These results may not hold in the non-commutative case.
Definition
The transpose of a matrix A, denoted by AT,[3] ⊤A, A⊤,
�
⊺{\displaystyle A^{\intercal }},[4][5] A′,[6] Atr, tA or At, may be constructed by any one of the following methods:

Reflect A over its main diagonal (which runs from top-left to bottom-right) to obtain AT
Write the rows of A as the columns of AT
Write the columns of A as the rows of AT
Formally, the i-th row, j-th column element of AT is the j-th row, i-th column element of A:

[
�
T
]
�
�
=
[
�
]
�
�
.
{\displaystyle \left[\mathbf {A} ^{\operatorname {T} }\right]_{ij}=\left[\mathbf {A} \right]_{ji}.}
If A is an m × n matrix, then AT is an n × m matrix.

In the case of square matrices, AT may also denote the Tth power of the matrix A. For avoiding a possible confusion, many authors use left upperscripts, that is, they denote the transpose as TA. An advantage of this notation is that no parentheses are needed when exponents are involved: as (TA)n = T(An), notation TAn is not ambiguous.

In this article this confusion is avoided by never using the symbol T as a variable name.

Matrix definitions involving transposition
A square matrix whose transpose is equal to itself is called a symmetric matrix; that is, A is symmetric if

�
T
=
�
.
{\displaystyle \mathbf {A} ^{\operatorname {T} }=\mathbf {A} .}
A square matrix whose transpose is equal to its negative is called a skew-symmetric matrix; that is, A is skew-symmetric if

�
T
=
−
�
.
{\displaystyle \mathbf {A} ^{\operatorname {T} }=-\mathbf {A} .}
A square complex matrix whose transpose is equal to the matrix with every entry replaced by its complex conjugate (denoted here with an overline) is called a Hermitian matrix (equivalent to the matrix being equal to its conjugate transpose); that is, A is Hermitian if

�
T
=
�
¯
.
{\displaystyle \mathbf {A} ^{\operatorname {T} }={\overline {\mathbf {A} }}.}
A square complex matrix whose transpose is equal to the negation of its complex conjugate is called a skew-Hermitian matrix; that is, A is skew-Hermitian if

�
T
=
−
�
¯
.
{\displaystyle \mathbf {A} ^{\operatorname {T} }=-{\overline {\mathbf {A} }}.}
A square matrix whose transpose is equal to its inverse is called an orthogonal matrix; that is, A is orthogonal if

�
T
=
�
−
1
.
{\displaystyle \mathbf {A} ^{\operatorname {T} }=\mathbf {A} ^{-1}.}
A square complex matrix whose transpose is equal to its conjugate inverse is called a unitary matrix; that is, A is unitary if

�
T
=
�
−
1
¯
.
{\displaystyle \mathbf {A} ^{\operatorname {T} }={\overline {\mathbf {A} ^{-1}}}.}
Examples
[
1
2
]
T
=
[
1
2
]
{\displaystyle {\begin{bmatrix}1&2\end{bmatrix}}^{\operatorname {T} }=\,{\begin{bmatrix}1\\2\end{bmatrix}}}
[
1
2
3
4
]
T
=
[
1
3
2
4
]
{\displaystyle {\begin{bmatrix}1&2\\3&4\end{bmatrix}}^{\operatorname {T} }={\begin{bmatrix}1&3\\2&4\end{bmatrix}}}
[
1
2
3
4
5
6
]
T
=
[
1
3
5
2
4
6
]
{\displaystyle {\begin{bmatrix}1&2\\3&4\\5&6\end{bmatrix}}^{\operatorname {T} }={\begin{bmatrix}1&3&5\\2&4&6\end{bmatrix}}}
Properties
Let A and B be matrices and c be a scalar.

(
�
T
)
T
=
�
.
{\displaystyle \left(\mathbf {A} ^{\operatorname {T} }\right)^{\operatorname {T} }=\mathbf {A} .}
The operation of taking the transpose is an involution (self-inverse).
(
�
+
�
)
T
=
�
T
+
�
T
.
{\displaystyle \left(\mathbf {A} +\mathbf {B} \right)^{\operatorname {T} }=\mathbf {A} ^{\operatorname {T} }+\mathbf {B} ^{\operatorname {T} }.}
The transpose respects addition.
(
�
�
)
T
=
�
T
�
T
.
{\displaystyle \left(\mathbf {AB} \right)^{\operatorname {T} }=\mathbf {B} ^{\operatorname {T} }\mathbf {A} ^{\operatorname {T} }.}
Note that the order of the factors reverses. From this one can deduce that a square matrix A is invertible if and only if AT is invertible, and in this case we have (A−1)T = (AT)−1. By induction, this result extends to the general case of multiple matrices, where we find that (A1A2…Ak−1Ak)T = AkTAk−1T…A2TA1T.
(
�
�
)
T
=
�
�
T
.
{\displaystyle \left(c\mathbf {A} \right)^{\operatorname {T} }=c\mathbf {A} ^{\operatorname {T} }.}
The transpose of a scalar is the same scalar. Together with (2), this states that the transpose is a linear map from the space of m × n matrices to the space of all n × m matrices.
det
(
�
T
)
=
det
(
�
)
.
{\displaystyle \det \left(\mathbf {A} ^{\operatorname {T} }\right)=\det(\mathbf {A} ).}
The determinant of a square matrix is the same as the determinant of its transpose.
The dot product of two column vectors a and b can be computed as the single entry of the matrix product:
[
�
⋅
�
]
=
�
T
�
,
{\displaystyle \left[\mathbf {a} \cdot \mathbf {b} \right]=\mathbf {a} ^{\operatorname {T} }\mathbf {b} ,}
which is written as ai bi in Einstein summation convention.
If A has only real entries, then ATA is a positive-semidefinite matrix.
(
�
T
)
−
1
=
(
�
−
1
)
T
.
{\displaystyle \left(\mathbf {A} ^{\operatorname {T} }\right)^{-1}=\left(\mathbf {A} ^{-1}\right)^{\operatorname {T} }.}
The transpose of an invertible matrix is also invertible, and its inverse is the transpose of the inverse of the original matrix. The notation A−T is sometimes used to represent either of these equivalent expressions.
If A is a square matrix, then its eigenvalues are equal to the eigenvalues of its transpose, since they share the same characteristic polynomial.
Products
If A is an m × n matrix and AT is its transpose, then the result of matrix multiplication with these two matrices gives two square matrices: A AT is m × m and AT A is n × n. Furthermore, these products are symmetric matrices. Indeed, the matrix product A AT has entries that are the inner product of a row of A with a column of AT. But the columns of AT are the rows of A, so the entry corresponds to the inner product of two rows of A. If pi j is the entry of the product, it is obtained from rows i and j in A. The entry pj i is also obtained from these rows, thus pi j = pj i, and the product matrix (pi j) is symmetric. Similarly, the product AT A is a symmetric matrix.

A quick proof of the symmetry of A AT results from the fact that it is its own transpose:

(
�
�
T
)
T
=
(
�
T
)
T
�
T
=
�
�
T
.
{\displaystyle \left(\mathbf {A} \mathbf {A} ^{\operatorname {T} }\right)^{\operatorname {T} }=\left(\mathbf {A} ^{\operatorname {T} }\right)^{\operatorname {T} }\mathbf {A} ^{\operatorname {T} }=\mathbf {A} \mathbf {A} ^{\operatorname {T} }.}[7]
Implementation of matrix transposition on computers
See also: In-place matrix transposition

Illustration of row- and column-major order
On a computer, one can often avoid explicitly transposing a matrix in memory by simply accessing the same data in a different order. For example, software libraries for linear algebra, such as BLAS, typically provide options to specify that certain matrices are to be interpreted in transposed order to avoid the necessity of data movement.

However, there remain a number of circumstances in which it is necessary or desirable to physically reorder a matrix in memory to its transposed ordering. For example, with a matrix stored in row-major order, the rows of the matrix are contiguous in memory and the columns are discontiguous. If repeated operations need to be performed on the columns, for example in a fast Fourier transform algorithm, transposing the matrix in memory (to make the columns contiguous) may improve performance by increasing memory locality.

Ideally, one might hope to transpose a matrix with minimal additional storage. This leads to the problem of transposing an n × m matrix in-place, with O(1) additional storage or at most storage much less than mn. For n ≠ m, this involves a complicated permutation of the data elements that is non-trivial to implement in-place. Therefore, efficient in-place matrix transposition has been the subject of numerous research publications in computer science, starting in the late 1950s, and several algorithms have been developed.

Transposes of linear maps and bilinear forms
See also: Transpose of a linear map
As the main use of matrices is to represent linear maps between finite-dimensional vector spaces, the transpose is an operation on matrices that may be seen as the representation of some operation on linear maps.

This leads to a much more general definition of the transpose that works on every linear map, even when linear maps cannot be represented by matrices (such as in the case of infinite dimensional vector spaces). In the finite dimensional case, the matrix representing the transpose of a linear map is the transpose of the matrix representing the linear map, independently of the basis choice.

Transpose of a linear map
Main article: Transpose of a linear map
Let X denote the algebraic dual space of an R-module X. Let X and Y be R-modules. If u : X → Y is a linear map, then its algebraic adjoint or dual,[8] is the map u : Y → X defined by f ↦ f ∘ u. The resulting functional u#(f) is called the pullback of f by u. The following relation characterizes the algebraic adjoint of u[9]

⟨u(f), x⟩ = ⟨f, u(x)⟩ for all f ∈ Y and x ∈ X
where ⟨•, •⟩ is the natural pairing (i.e. defined by ⟨h, z⟩ := h(z)). This definition also applies unchanged to left modules and to vector spaces.[10]

The definition of the transpose may be seen to be independent of any bilinear form on the modules, unlike the adjoint (below).

The continuous dual space of a topological vector space (TVS) X is denoted by X'. If X and Y are TVSs then a linear map u : X → Y is weakly continuous if and only if u(Y') ⊆ X', in which case we let tu : Y' → X' denote the restriction of u to Y'. The map tu is called the transpose[11] of u.

If the matrix A describes a linear map with respect to bases of V and W, then the matrix AT describes the transpose of that linear map with respect to the dual bases.

Transpose of a bilinear form
Main article: Bilinear form
Every linear map to the dual space u : X → X defines a bilinear form B : X × X → F, with the relation B(x, y) = u(x)(y). By defining the transpose of this bilinear form as the bilinear form tB defined by the transpose tu : X → X i.e. tB(y, x) = tu(Ψ(y))(x), we find that B(x, y) = tB(y, x). Here, Ψ is the natural homomorphism X → X## into the double dual.

Adjoint
Not to be confused with Hermitian adjoint.
If the vector spaces X and Y have respectively nondegenerate bilinear forms BX and BY, a concept known as the adjoint, which is closely related to the transpose, may be defined:

If u : X → Y is a linear map between vector spaces X and Y, we define g as the adjoint of u if g : Y → X satisfies

�
�
(
�
,
�
(
�
)
)
=
�
�
(
�
(
�
)
,
�
)
{\displaystyle B_{X}{\big (}x,g(y){\big )}=B_{Y}{\big (}u(x),y{\big )}} for all x ∈ X and y ∈ Y.
These bilinear forms define an isomorphism between X and X, and between Y and Y, resulting in an isomorphism between the transpose and adjoint of u. The matrix of the adjoint of a map is the transposed matrix only if the bases are orthonormal with respect to their bilinear forms. In this context, many authors however, use the term transpose to refer to the adjoint as defined here.

The adjoint allows us to consider whether g : Y → X is equal to u −1 : Y → X. In particular, this allows the orthogonal group over a vector space X with a quadratic form to be defined without reference to matrices (nor the components thereof) as the set of all linear maps X → X for which the adjoint equals the inverse.

Over a complex vector space, one often works with sesquilinear forms (conjugate-linear in one argument) instead of bilinear forms. The Hermitian adjoint of a map between such spaces is defined similarly, and the matrix of the Hermitian adjoint is given by the conjugate transpose matrix if the bases are orthonormal.

See also
Adjugate matrix, the transpose of the cofactor matrix
Conjugate transpose
Moore–Penrose pseudoinverse
Projection (linear algebra)
References
Nykamp, Duane. "The transpose of a matrix". Math Insight. Retrieved September 8, 2020.
Arthur Cayley (1858) "A memoir on the theory of matrices", Philosophical Transactions of the Royal Society of London, 148 : 17–37. The transpose (or "transposition") is defined on page 31.
T.A. Whitelaw (1 April 1991). Introduction to Linear Algebra, 2nd edition. CRC Press. ISBN 978-0-7514-0159-2.
"Transpose of a Matrix Product (ProofWiki)". ProofWiki. Retrieved 4 Feb 2021.
"What is the best symbol for vector/matrix transpose?". Stack Exchange. Retrieved 4 Feb 2021.
Weisstein, Eric W. "Transpose". mathworld.wolfram.com. Retrieved 2020-09-08.
Gilbert Strang (2006) Linear Algebra and its Applications 4th edition, page 51, Thomson Brooks/Cole ISBN 0-03-010567-6
Schaefer & Wolff 1999, p. 128.
Halmos 1974, §44
Bourbaki 1989, II §2.5
Trèves 2006, p. 240.
Further reading
Bourbaki, Nicolas (1989) [1970]. Algebra I Chapters 1-3 [Algèbre: Chapitres 1 à 3] (PDF). Éléments de mathématique. Berlin New York: Springer Science & Business Media. ISBN 978-3-540-64243-5. OCLC 18588156.
Halmos, Paul (1974), Finite dimensional vector spaces, Springer, ISBN 978-0-387-90093-3.
Maruskin, Jared M. (2012). Essential Linear Algebra. San José: Solar Crest. pp. 122–132. ISBN 978-0-9850627-3-6.
Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.
Trèves, François (2006) [1967]. Topological Vector Spaces, Distributions and Kernels. Mineola, N.Y.: Dover Publications. ISBN 978-0-486-45352-1. OCLC 853623322.
Schwartz, Jacob T. (2001). Introduction to Matrices and Vectors. Mineola: Dover. pp. 126–132. ISBN 0-486-42000-0.
External links
Gilbert Strang (Spring 2010) Linear Algebra from MIT Open Courseware
vte
Linear algebra
vte
Tensors
Categories: MatricesAbstract algebraLinear algebra
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Chud Fri 15 Sep 2023 12:35:52 No.151882 Report

>>151879
unintelligible sir

Chud Fri 15 Sep 2023 12:36:26 No.151883 Report

>>151881
marge

Chud Fri 15 Sep 2023 12:36:26 No.151884 Report

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WikipediaThe Free Encyclopedia
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Contents hide
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Name
Species having the common name "nightshade"
Food crops
Ornamentals
Medicine
Ecology
Systematics
Toggle Systematics subsection
Subgenus Bassovia
Subgenus Leptostemonum
Subgenus Lyciosolanum
Subgenus Solanum sensu stricto
Other notable species
Formerly placed here
References
External links
Solanum

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From Wikipedia, the free encyclopedia
For other uses, see Solanum (disambiguation).
"Horsenettle" and variants redirect here. If used for a particular species, this name usually applies to the Carolina horsenettle (S. carolinense)
Solanum

Brazilian nightshade (Solanum seaforthianum)
Scientific classificationEdit this classification
Kingdom:Plantae
Clade:Tracheophytes
Clade:Angiosperms
Clade:Eudicots
Clade:Asterids
Order:Solanales
Family:Solanaceae
Subfamily:Solanoideae
Tribe:Solaneae
Genus:Solanum
L.[1]
Type species
Solanum nigrum L.[2]
Subgenera
Bassovia
Leptostemonum
Lyciosolanum
Solanum
(but see text)

Synonyms
Androcera Nutt.
Aquartia Jacq.
Artorhiza Raf.
Bassovia Aubl.
Battata Hill
Bosleria A.Nelson
Ceranthera Raf.
Cliocarpus Miers
Cyphomandra Mart. ex Sendtn.
Diamonon Raf.
Dulcamara Moench
Lycopersicon Mill.
Melongena Mill.
Normania Lowe
Nycterium Vent.
Ovaria Fabr.
Parmentiera Raf. (non DC.: preoccupied)
Petagnia Raf.
Pionandra Miers
Pheliandra Werderm.
Pseudocapsicum Medik.
Scubulus Raf.
Solanastrum Fabr.
Solanocharis Bitter
Solanopsis Bitter
Triguera Cav.

Unripe fruit of Solanum lycopersicum (tomato)
Solanum is a large and diverse genus of flowering plants, which include three food crops of high economic importance: the potato, the tomato and the eggplant (aubergine, brinjal). It is the largest genus in the nightshade family Solanaceae, comprising around 1,500 species. It also contains the so-called horse nettles (unrelated to the genus of true nettles, Urtica), as well as numerous plants cultivated for their ornamental flowers and fruit.

Solanum species show a wide range of growth habits, such as annuals and perennials, vines, subshrubs, shrubs, and small trees. Many formerly independent genera like Lycopersicon (the tomatoes) and Cyphomandra are now included in Solanum as subgenera or sections. Thus, the genus today contains roughly 1,500–2,000 species.

Name
The generic name was first used by Pliny the Elder (AD 23–79) for a plant also known as strychnos, most likely S. nigrum. Its derivation is uncertain, possibly stemming from the Latin word sol, meaning "sun", referring to its status as a plant of the sun.[3]

Species having the common name "nightshade"
The species most commonly called nightshade in North America and Britain is Solanum dulcamara, also called bittersweet or woody nightshade (so-called because it is a (scandent) shrub). Its foliage and egg-shaped red berries are poisonous, the active principle being solanine, which can cause convulsions and death if taken in large doses. Black nightshade (Solanum nigrum) is also generally considered poisonous, but its fully-ripened fruit and its foliage are both cooked and eaten in some areas. Deadly nightshade (Atropa belladonna) belongs, like Solanum, to subfamily Solanoideae of the nightshade family, but, unlike that genus, is a member of tribe Hyoscyameae (Solanum belongs to tribe Solaneae).[4] The chemistry of Atropa species is very different from that of Solanum species and features the very toxic tropane alkaloids, the best-known of which is atropine.[5]

Food crops
Most parts of the plants, especially the green parts and unripe fruit, are poisonous to humans (although not necessarily to other animals), but many species in the genus bear some edible parts, such as fruits, leaves, or tubers. Three crops in particular have been bred and harvested for consumption by humans for centuries, and are now cultivated on a global scale:

Tomato, S. lycopersicum
Tomato varieties are sometimes bred from both S. lycopersicum and wild tomato species such as S. pimpinellifolium, S. peruvianum, S. cheesmanii, S. galapagense, S. chilense, etc. (such varieties include—among others—Bicentennial, Dwarf Italian, Epoch, Golden Sphere, Hawaii, Ida Red, Indigo Rose,[6] Kauai, Lanai, Marion, Maui, Molokai, Niihau, Oahu, Owyhee, Parma, Payette, Red Lode, Super Star, Surecrop, Tuckers Forcing, V 121, Vantage, Vetomold, and Waltham.)[7]
Potato, S. tuberosum, fourth largest food crop.
Less important but cultured relatives used in small amounts include S. stenotomum, S. phureja, S. goniocalyx, S. ajanhuiri, S. chaucha, S. juzepczukii, S. curtilobum.
Eggplant (also known as brinjal or aubergine), S. melongena
Other species are significant food crops regionally, such as Ethiopian eggplant or gilo (S. aethiopicum), naranjilla or lulo (S. quitoense), Turkey berry (S. torvum), pepino or pepino melon (S. muricatum), Tamarillo (S. betaceum), wolf apple (S. lycocarpum), garden huckleberry (S. scabrum) and "bush tomatoes" (several Australian species).

Ornamentals
The species most widely seen in cultivation as ornamental plants are:

S. aviculare (kangaroo apple)
S. capsicastrum (false Jerusalem cherry, winter cherry)
S. crispum (Chilean potato tree)
S. laciniatum (kangaroo apple)
S. laxum (potato vine)
S. mammosum (Nipplefruit, titty fruit, cow's udder, apple of Sodom)
S. pseudocapsicum (Christmas cherry, winter cherry)
S. rantonnetii (blue potato bush)
S. seaforthianum (Italian jasmine, St. Vincent lilac)
S. mauritianum (woolly nightshade, earleaf nightshade)
S. wendlandii (paradise flower, potato vine)[8]
Medicine
Poisonings associated with certain species of Solanum are not uncommon and may be fatal. However, several species are locally used in folk medicine, particularly by native people who have long employed them.

Ecology
Solanum species are used as food plants by the larvae of some Lepidoptera species (butterflies and moths) – see list of Lepidoptera that feed on Solanum.

Systematics
See also: List of Solanum species
The genus was established by Carl Linnaeus in 1753.[9] Its subdivision has always been problematic, but slowly some sort of consensus is being achieved.

The following list is a provisional lineup of the genus' traditional subdivisions, together with some notable species.[9] Many of the subgenera and sections might not be valid; they are used here provisionally as the phylogeny of this genus is not fully resolved yet and many species have not been reevaluated.

Cladistic analyses of DNA sequence data suggest that the present subdivisions and rankings are largely invalid. Far more subgenera would seem to warrant recognition, with Leptostemonum being the only one that can at present be clearly subdivided into sections. Notably, it includes as a major lineage several members of the traditional sections Cyphomandropsis and the old genus Cyphomandra.[1]

Subgenus Bassovia
Section Allophylla

Solanum granuloso-leprosum
Section Cyphomandropsis

Solanum glaucophyllum Desf. – Waxy-leaved nightshade
Section Pachyphylla

Solanum betaceum Cav. – Tamarillo
Solanum exiguum
Solanum roseum
Subgenus Leptostemonum

Five-minute plant (S. atropurpureum) fruit

Solanum palinacanthum

Shrubby nightshade (S. robustum) flowers

Giant potatocreeper (S. wendlandii) flowers

Porcupine tomato (S. pyracanthos) fruit
Section Acanthophora

Solanum aculeatissimum Jacq. – Indian nightshade
Solanum atropurpureum Schrank – Five-minute plant
Solanum capsicoides – Cockroach berry, polohauaiʻi (Polynesian)
Solanum mammosum – Nipplefruit, titty fruit, cow's udder, "apple of Sodom"
Solanum palinacanthum Dunal
Solanum viarum Dunal – Tropical soda apple
Section Androceras: 12 spp.[10]

Series Androceras
Series Violaceiflorum
Series Pacificum
Section Anisantherum
Section Campanulata
Section Crinitum
Section Croatianum
Section Erythrotrichum

Solanum robustum H.L.Wendl. – Shrubby nightshade
Section Graciliflorum[verification needed]
Section Herposolanum

Solanum wendlandii Hook.f. – Giant potatocreeper
Section Irenosolanum

Solanum incompletum Dunal – Pōpolo kū mai (Hawaiʻi)
Solanum nelsonii Dunal – Nelson's horsenettle, ʻĀkia (Hawaiʻi)
Solanum sandwicense Hook. & Arn. – Hawaiian horsenettle, Pōpoloʻaiakeakua (Oʻahu, Kauaʻi)
Section Ischyracanthum
Section Lasiocarpa

Solanum lasiocarpum Dunal
Solanum pseudolulo – lulo de perro (Colombia)
Solanum quitoense – lulo (Colombia), naranjilla (Ecuador)
Solanum sessiliflorum – Cocona
Section Melongena

Solanum aculeastrum – Soda apple, sodaapple nightshade, goat apple, poison apple, "bitter-apple"
Solanum campechiense – Redberry nightshade
Solanum carolinense – Carolina horsenettle, radical weed, sand brier, devil's tomato, "bull nettle", "tread-softly", "apple of Sodom", "wild tomato" (southeastern United States)
Solanum cataphractum (northern Western Australia, including Coronation Island)[11]
Solanum citrullifolium A.Braun – Watermelon nightshade (southern United States)
Solanum dimidiatum Raf. – Torrey's nightshade
Solanum elaeagnifolium – Silver-leaved nightshade, prairie berry, silverleaf nettle, white horsenettle, silver nightshade, "bull-nettle", "trompillo" (Spanish); Silver-leaf bitter-apple, satansbos (South Africa)
Solanum heterodoxum Dunal – Melon-leaved nightshade
Solanum incanum L.
Solanum linnaeanum – Devil's apple, "apple of Sodom"
Solanum macrocarpon L.
Solanum marginatum L.f. – White-margined nightshade
Solanum melongena – Eggplant, aubergine (including S. ovigerum)
Solanum rostratum Dunal – Buffalo bur, Texas thistle
Solanum sisymbriifolium Lam. – Sticky nightshade, fire-and-ice
Solanum virginianum L.
Section Micracantha

Solanum jamaicense Mill. – Jamaican nightshade
Solanum lanceifolium Jacq. – Lance-leaved nightshade
Solanum tampicense Dunal – Wetland nightshade
Section Monodolichopus
Section Nycterium
Section Oliganthes

Solanum aethiopicum – Ethiopian eggplant, nakati, mock tomato, Ethiopian nightshade; including S. gilo (scarlet eggplant, Gilo or jiló)
Solanum centrale – Australian desert raisin, bush raisin, bush sultana, "bush tomato", akatjurra (Alyawarre), kampurarpa (Pitjantjatjara), merne akatyerre (Arrernte), kutjera
Solanum cleistogamum – "bush tomato", merne mwanyerne (Arrernte)
Solanum ellipticum – Potato bush, "bush tomato"
Solanum pyracanthos Lam. – Porcupine tomato, Devil's Thorn
Solanum quadriloculatum F.Muell. – "bush tomato", "wild tomato" (Australia)
Section Persicariae

Solanum bahamense L. – Bahama nightshade, canker berry, berengena de playa
Solanum ensifolium Dunal – Erubia
Section Polytrichum
Section Pugiunculifera
Section Somalanum
Section Torva

Solanum asteropilodes
Solanum chrysotrichum Schltdl. – Giant devil's-fig
Solanum lanceolatum – Orangeberry nightshade
Solanum paniculatum – Jurubeba
Solanum torvum – Turkey berry, devil's fig, prickly nightshade, shoo-shoo bush, wild eggplant, pea eggplant
Subgenus Lyciosolanum
Solanum guineense L.
Subgenus Solanum sensu stricto

Solanum erianthum

Jasmine nightshade (S. laxum) flowers

Currant tomato (S. pimpinellifolium) fruit

Andean black potatoes (S. tuberosum)

Turkey berry (S. torvum) flowers

Yellow nightshade (S. villosum) fruit
Section Afrosolanum
Section Anarrhichomenum

Solanum baretiae[12]
Section Archaesolanum

Solanum aviculare – Poroporo (New Zealand), kangaroo apple (Australia)
Section Basarthrum

Solanum catilliflorum[13]
Solanum muricatum – Pepino dulce, pepino melon, melon pear, "pepino", "tree melon"
Solanum perlongistylum[13]
Solanum tergosericeum[14]
Section Benderianum
Section Brevantherum

Solanum bullatum
Solanum erianthum D.Don – Potato tree, "mullein nightshade"
Solanum mauritianum – Woolly nightshade, ear-leaved nightshade, flannel weed, bugweed, tobacco weed, kerosene plant, "wild tobacco" (Australia)
Solanum evolvuloides
Section Dulcamara

Solanum crispum – Chilean potato vine, Chilean nightshade, Chilean potato tree
Solanum dulcamara – Bittersweet
Solanum imbaburense
Solanum laxum Spreng. – Jasmine nightshade
Solanum leiophyllum
Solanum seaforthianum Andrews – Brazilian nightshade
Solanum triquetrum Cav. – Texas nightshade
Solanum wallacei – Wallace's nightshade, Catalina nightshade, Clokey's nightshade, "wild tomato" (including S. clokeyi)
Solanum xanti – Purple nightshade, San Diego nightshade
Section Herpystichum
Section Holophylla

Solanum diphyllum L. – Twin-leaved nightshade
Solanum pseudocapsicum – Jerusalem cherry, Madeira winter cherry, "winter cherry" (including S. capsicastrum)
Solanum pseudoquina (including S. inaequale Vell.)
Section Juglandifolia

Solanum juglandifolium
Solanum ochranthum
Section Lemurisolanum
Section Lycopersicoides

Solanum lycopersicoides Dunal – Peruvian wolfpeach
Solanum sitiens
Section Lycopersicon

Solanum arcanum Peralta – "wild tomato"
Solanum chilense
Solanum corneliomulleri
Solanum huaylasense Peralta
Solanum peruvianum L. – Peruvian nightshade, "wild tomato"
Solanum cheesmaniae (L.Riley) Fosberg
Solanum chmielewskii
Solanum galapagense S.C.Darwin & Peralta
Solanum habrochaites
Solanum lycopersicum – Tomato
Solanum neorickii
Solanum pennellii
Solanum pimpinellifolium – Currant tomato
Section Macronesiotes
Section Normania
†Solanum nava (?)
Section Petota

Solanum albornozii
Solanum bulbocastanum – Ornamental nightshade
Solanum bukasovii Juz. ex Rybin
Solanum burtonii
Solanum cardiophyllum – Heart-leaved nightshade
Solanum chilliasense
Solanum commersonii Dunal – Commerson's nightshade
Solanum demissum Lindl. – Dwarf wild potato
Solanum jamesii – Wild potato
Solanum minutifoliolum
Solanum paucijugum
Solanum phureja Juz. & Bukasov
Solanum pinnatisectum Dunal – Tansy-leaved nightshade
Solanum regularifolium
Solanum stoloniferum Schltdl. – Tigna potato, Fendler's horsenettle
Solanum stenotomum (including S. goniocalyx)
Solanum ternatum (including S. ternifolium)
Solanum tuberosum – Potato
Section Pteroidea
Section Quadrangulare
Section Regmandra
Section Solanum

Solanum adscendens Sendtner – Sonoita nightshade (Americas)
Solanum americanum Mill. – American nightshade, American black nightshade, glossy nightshade (Americas, Hawaiʻi)
Solanum chenopodioides Lam. – Goosefoot nightshade, slender nightshade (including S. gracilius)
Solanum douglasii Dunal – Green-spotted nightshade
Solanum interius Rydb.
Solanum melongena L.[15]
Solanum nigrescens M.Martens & Galeotti – Divine nightshade
Solanum nigrum L. – European black nightshade, "black nightshade"
S. nigrum guineense – "Garden Huckleberry"
Solanum pseudogracile Heiser – Glowing nightshade
Solanum ptychanthum – West Indian nightshade, Eastern black nightshade
Solanum retroflexum – Wonderberry, sunberry
Solanum sarrachoides – Hairy nightshade
Solanum scabrum Mill. – Garden huckleberry
Solanum triflorum Nutt. – Cut-leaved nightshade
Solanum villosum Mill. – Yellow nightshade
Other notable species

Forked nightshade (S. furcatum)

Bluewitch nightshade (S. umbelliferum) flowers
Solanum abutiloides – Dwarf tamarillo
Solanum amygdalifolium Steud.
Solanum bellum
Solanum cajanumense
Solanum chimborazense
Solanum chrysasteroides
Solanum cinnamomeum
Solanum conocarpum Rich. ex Dunal – Marron bacoba
Solanum cowiei Martine
Solanum cremastanthemum
Solanum davisense Whalen – Davis' horsenettle
Solanum densepilosulum
Solanum donianum Walp. – Mullein nightshade
Solanum dolichorhachis
Solanum fallax
Solanum ferox L. – Hairy-fruited eggplant, Thai hairy-fruited eggplant
Solanum fortunense
Solanum furcatum – Forked nightshade
Solanum glabratum Dunal
Solanum haleakalaense H.St.John
Solanum hindsianum Benth. – Hinds' nightshade
Solanum hypermegethes
Solanum hypocalycosarcum
Solanum interandinum
Solanum latiflorum
Solanum leucodendron
Solanum lumholtzianum Bartlett – Sonoran nightshade
Solanum luteoalbum (including S. semicoalitum)
Solanum lycocarpum – Wolf apple, fruta-de-lobo, lobeira (Brazil)
Solanum melissarum Bohs
Solanum nudum Dunal – Forest nightshade
Solanum ovum-fringillae
Solanum paralum
Solanum parishii A.Heller – Parish's nightshade
Solanum physalifolium Rusby
Solanum pinetorum
Solanum polygamum Vahl – Cakalaka berry
Solanum pyrifolium Lam.
Solanum pubescens Willd.
Solanum riedlei Dunal – Riedle's nightshade
Solanum rudepannum Dunal
Solanum rugosum Dunal – tabacon aspero
Solanum sibundoyense
Solanum sodiroi (including S. carchiense)
Solanum sycocarpum
Solanum tenuipes Bartlett – Fancy nightshade
Solanum tobagense
Solanum trilobatum L.
Solanum umbelliferum – Bluewitch nightshade
Solanum violaceum Ortega
Solanum viride Spreng. – Green Nightshade
Solanum woodburyi Howard – Woodbury's nightshade
Formerly placed here

Lycianthes rantonnetii and its congeners were often placed in Solanum
Some plants of other genera were formerly placed in Solanum:

Chamaesaracha coronopus (as S. coronopus)
Lycianthes biflora (as S. multifidum Buch.-Ham. ex D.Don)
Lycianthes denticulata (as S. gouakai var. angustifolium and var. latifolium)
Lycianthes lycioides (as S. lycioides var. angustifolium)
Lycianthes mociniana (as S. uniflorum Dunal in Poir. and S. uniflorum Sessé & Moc.)
Lycianthes rantonnetii (as S. rantonnetii, S. urbanum var. ovatifolium and var. typicum)
Undetermined species of Lycianthes have been referred to under names such as S. chrysophyllum, S. ciliatum Blume ex Miq., S. corniculatum Hiern, S. lanuginosum, S. mucronatum, S. retrofractum var. acuminatum, S. violaceum Blume, S. violifolium f. typicum, S. virgatum notst β albiflorum, S. uniflorum Lag. or S. uniflorum var. berterianum.
References
"Solanum L." Germplasm Resources Information Network. United States Department of Agriculture. 2009-09-01. Retrieved 2013-07-15.
Solanum | International Plant Names Index. (n.d.). Retrieved August 11, 2023, from https://www.ipni.org/n/30000630-2
Quattrocchi, U. (2000). CRC World Dictionary of Plant Names: Vol. 4, R-Z. Taylor and Francis. p. 2058. ISBN 978-0-8493-2678-3.
Armando T. Hunziker 2001: The Genera of Solanaceae. A.R.G. Gantner Verlag, Ruggell, Liechtenstein. ISBN 3-904144-77-4.
Frohne, Dietrich and Pfänder, Hans Jürgen. 1984 A Colour Atlas of Poisonous Plants : A Handbook for Pharmacists, Doctors, Toxicologists, and Biologists transl. from 2nd German ed. by Norman Grainger Bisset, London : Wolfe Atlases. Wolfe Publishing.
"Purple tomato debuts as 'Indigo Rose'". Extension Service. Oregon state university. 2012-01-27. Retrieved 2018-06-25.
"Vegetable Cultivar Descriptions for North America | Cucurbit Breeding". NCSU. Retrieved 2018-06-25.
RHS A-Z encyclopedia of garden plants. United Kingdom: Dorling Kindersley. 2008. p. 1136. ISBN 978-1405332965.
"Solanum Phylogeny". Solanaceae Source. Natural History Museum. Retrieved 2009-11-01.
Whalen, Michael D (1979). "Allozyme Variation and Evolution in Solanum Section Androceras". Systematic Botany. 4 (3): 203–222. doi:10.2307/2418419. JSTOR 2418419.
"Factsheet – Solanum cataphractum". Electronic Flora of South Australia. Retrieved 8 November 2020.
Tepe, E. J.; Ridley, G.; Bohs, L. (2012). "A new species of Solanum named for Jeanne Baret, an overlooked contributor to the history of botany". PhytoKeys (8): 37–47. doi:10.3897/phytokeys.8.2101. PMC 3254248. PMID 22287929.
Anderson, G. J.; Martine, C. T.; Prohens, J.; Nuez, F. (2006). "Solanum perlongistylum and S. catilliflorum, New Endemic Peruvian Species of Solanum, Section Basarthrum, Are Close Relatives of the Domesticated Pepino, S. muricatum". Novon. 16 (2): 161–67. doi:10.3417/1055-3177(2006)16[161:SPASCN]2.0.CO;2. ISSN 1055-3177. S2CID 85629504.
Ochoa, C. M. (2006). "Solanum tergosericeum (Solanaceae sect. Basarthrum): A new species from Peru" (PDF). Phytologia. 88 (2): 212–15. doi:10.5962/bhl.part.27433.
Reina, Antonio Maria MARTINEZ; Zumaqué, Lilibeth Tordecilla; Martínez, Liliana María Grandett; Pinto, María del Valle Rodríguez (2020-08-25). "Adopcion Adopción de la variedad de berenjena C015 (Solanum melongena L.) en la región Caribe colombiana: measuring adoption". Ciencia y Agricultura (in Spanish). 17 (3): 1–10. doi:10.19053/01228420.v17.n3.2020.11062. ISSN 2539-0899. S2CID 225303476.
External links
Media related to Solanum at Wikimedia Commons
Data related to Solanum at Wikispecies
Dressler, S.; Schmidt, M. & Zizka, G. (2014). "Solanum". African plants – a Photo Guide. Frankfurt/Main: Forschungsinstitut Senckenberg.
Meet the TomTato: Tomatoes and potatoes grown as one – CBS News (September 26, 2013)
Taxon identifiers
Wikidata: Q146555Wikispecies: SolanumAPDB: 194953APNI: 80674BOLD: 7060CoL: 63SD9eFloraSA: SolanumEoL: 590245EPPO: 1SOLGFloraBase: 22038FoAO2: SolanumFoC: 130618Fossilworks: 319863GBIF: 2928997GRIN: 11264iNaturalist: 50641IPA: 13322IPNI: 99597-3IRMNG: 1340412ITIS: 30412NBN: NHMSYS0000463743NCBI: 4107NZOR: 3d593a97-9390-4498-9090-7bc3241f3f2cOpen Tree of Life: 1020645PLANTS: SOLANPOWO: urn:lsid:ipni.org:names:30000630-2Tropicos: 40001681VASCAN: 1696VicFlora: 2557555f-7c74-48bc-bb1d-286fe65f860fWFO: wfo-4000035688
Categories: SolanumSolanaceae generaMedicinal plants
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