JuliaWSMatrix E

jwsagg.spad line 339 [edit on github]

Julia Wolfram Symbolic matrices using Wolfram Symbolic Transport Protocol.

#: % -> JuliaWSInteger

from JuliaWSAggregate JuliaWSVector E

#: % -> NonNegativeInteger

from Aggregate

*: (%, %) -> %

a * b is the matrix multiplication, not the element-wise multiplication. WS error if dimensions are incompatible.

*: (%, E) -> %

x * r is the right scalar multiple of the scalar r and the matrix x.

*: (%, JuliaWSVector E) -> %

x * c is the product of the matrix x and the column vector c. Error: if the dimensions are incompatible.

*: (%, JuliaWSVector E) -> JuliaWSVector E

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

*: (E, %) -> %

r*x is the left scalar multiple of the scalar r and the matrix x.

*: (Integer, %) -> %

n*a scale the matrix a by n.

*: (JuliaWSVector E, %) -> %

r * x is the product of the row vector r and the matrix x. Error: if the dimensions are incompatible.

*: (JuliaWSVector E, %) -> JuliaWSVector E

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

+: (%, %) -> %

a + b is the matrix addition. WS error if dimensions are incompatible.

-: % -> %

-a negates each elements of the matrix a.

-: (%, %) -> %

a - b is the matrix substraction. WS error if dimensions are incompatible.

/: (%, E) -> % if E has Field

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

=: (%, %) -> Boolean

from BasicType

^: (%, Integer) -> % if E has Field

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

^: (%, NonNegativeInteger) -> %

a^n is the matrix power by the non negative integer n.

^: (%, PositiveInteger) -> %

a^n is the matrix power by the positive integer n.

~=: (%, %) -> Boolean

from BasicType

accumulate: % -> % if JuliaWSVector E has JuliaWSNumber

from JuliaWSAggregate JuliaWSVector E

adjoint: % -> %

adjoint(m) returns the adjoint of m, i.e. the conjugate transposition of m.

adjugate: % -> %

adjugate(m) returns the adjugate of square m.

antisymmetric?: % -> Boolean

antisymmetric?(m) returns true if the matrix m is square and antisymmetric (i.e. m[i, j] = -m[j, i] for all i and j) and false otherwise.

any?: (E -> Boolean, %) -> Boolean

from HomogeneousAggregate E

append: (%, JuliaWSVector E) -> %

from JuliaWSAggregate JuliaWSVector E

array2: List List E -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

blockConcat: List List % -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

blockSplit: (%, List NonNegativeInteger, List NonNegativeInteger) -> List List %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

blockSplit: (%, PositiveInteger, PositiveInteger) -> List List %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

cholesky: % -> Record(l: %, u: %)

cholesky(m) computes the Cholesky decomposition of the square matrix m.

coerce: % -> JuliaWSExpression

from JuliaWSAggregate JuliaWSVector E

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: JuliaWSVector E -> %

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

coerce: List JuliaWSVector E -> %

from JuliaWSAggregate JuliaWSVector E

colSlice: % -> Segment Integer

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

column: (%, Integer) -> %

column(mat,i) returns the i-th column.

column: (%, Integer) -> JuliaWSVector E

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

columnSpace: % -> List JuliaWSVector E if E has EuclideanDomain

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

convert: % -> String

from ConvertibleTo String

copy: % -> %

from Aggregate

count: (E -> Boolean, %) -> NonNegativeInteger

from HomogeneousAggregate E

count: (E, %) -> NonNegativeInteger

from HomogeneousAggregate E

delete: (%, JuliaWSList JuliaWSInteger) -> %

from JuliaWSAggregate JuliaWSVector E

determinant: % -> E if E has CommutativeRing

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

diagonal?: % -> Boolean

diagonal?(m) returns true if the matrix m is square and diagonal (i.e. all entries of m not on the diagonal are zero) and false otherwise.

diagonal: % -> JuliaWSVector E

diagonal(m) returns the diagonal elements of m as a vector.

diagonalMatrix: JuliaWSList E -> %

diagonalMatrix(l) returns a diagonal matrix with elements of l as diagonal elements.

diagonalMatrix: List % -> %

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

diagonalMatrix: List E -> %

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

differences: % -> % if JuliaWSVector E has JuliaWSNumber

from JuliaWSAggregate JuliaWSVector E

dimensions: % -> JuliaWSList JuliaWSInteger

from JuliaWSAggregate JuliaWSVector E

eigenSystem: % -> Record(values: JuliaWSVector JuliaWSExpression, vectors: JuliaWSMatrix JuliaWSExpression)

eigenSystem(m) computes the spectral decomposition of the square matrix m. It returns in a Record, the eigenvalues, selector ‘values’, and the eigenvectors selector ‘vectors’.

eigenvalues: % -> JuliaWSVector JuliaWSExpression

eigenvalues(m) returns the eigenvalues of the square matrix m.

eigenvectors: % -> JuliaWSMatrix JuliaWSExpression

eigenvectors(m) returns the eigenvectors of the square matrix m.

elt: (%, Integer) -> JuliaWSVector E

from JuliaWSAggregate JuliaWSVector E

elt: (%, Integer, Integer) -> E

elt(mat, m, n) returns the element (m,n) of the matrix mat.

elt: (%, Integer, Integer, E) -> E

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

elt: (%, Integer, List Integer) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

elt: (%, Integer, List Segment Integer) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

elt: (%, List Integer, Integer) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

elt: (%, List Integer, List Integer) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

elt: (%, List Integer, Segment Integer) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

elt: (%, List Segment Integer, Integer) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

elt: (%, List Segment Integer, List Segment Integer) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

elt: (%, List Segment Integer, Segment Integer) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

elt: (%, Segment Integer, List Integer) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

elt: (%, Segment Integer, List Segment Integer) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

elt: (%, Segment Integer, Segment Integer) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

empty?: % -> Boolean

from Aggregate

empty: () -> %

from Aggregate

eq?: (%, %) -> Boolean

from Aggregate

eval: (%, E, E) -> % if E has Evalable E

from InnerEvalable(E, E)

eval: (%, Equation E) -> % if E has Evalable E

from Evalable E

eval: (%, List E, List E) -> % if E has Evalable E

from InnerEvalable(E, E)

eval: (%, List Equation E) -> % if E has Evalable E

from Evalable E

every?: (E -> Boolean, %) -> Boolean

from HomogeneousAggregate E

exquo: (%, E) -> Union(%, failed) if E has IntegralDomain

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

extract: (%, JuliaWSExpression) -> %

from JuliaWSAggregate JuliaWSVector E

fill!: (%, E) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

first: % -> JuliaWSVector E

from JuliaWSAggregate JuliaWSVector E

generalizedInverse: % -> %

generalizedInverse(m) computes the pseudo inverse of m also knows as Moore-Penrose inverse.

hash: % -> SingleInteger if E has Hashable

from Hashable

hashUpdate!: (HashState, %) -> HashState if E has Hashable

from Hashable

hermitian?: % -> Boolean

hermitian?(m) checks whether or not m is hermitian.

hessenberg: % -> Record(p: %, h: %)

hessenberg(m) computes the Hessenberg decomposition of the square matrix m.

horizConcat: (%, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

horizConcat: List % -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

horizSplit: (%, List NonNegativeInteger) -> List %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

horizSplit: (%, PositiveInteger) -> List %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

insert: (%, JuliaWSVector E, JuliaWSInteger) -> %

from JuliaWSAggregate JuliaWSVector E

intersection: (%, %) -> %

from JuliaWSAggregate JuliaWSVector E

inverse: % -> %

inverse(m) computes the inverse of m. For example: example{m:=jWSMatrix(”{{a, b}, {b, a}}”)@JWSMAT(JWSEXPR)} example{inverse m}

inverse: % -> Union(%, failed) if E has Field

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

invertIfCan: % -> Union(%, failed) if E has IntegralDomain

invertIfCan(m) returns the inverse of the matrix m. If the matrix is not invertible, “failed” is returned. Error: if the matrix is not square.

jlAbout: % -> Void

from JuliaObjectType

jlApply: (String, %) -> %

from JuliaObjectType

jlApply: (String, %, %) -> %

from JuliaObjectType

jlApply: (String, %, %, %) -> %

from JuliaObjectType

jlApply: (String, %, %, %, %) -> %

from JuliaObjectType

jlApply: (String, %, %, %, %, %) -> %

from JuliaObjectType

jlApply: (String, %, %, %, %, %, %) -> %

from JuliaObjectType

jlEval: % -> %

from JuliaWSObject

jlHead: % -> JuliaWSSymbol

from JuliaWSObject

jlId: % -> String

from JuliaObjectType

jlNumeric: % -> %

from JuliaWSObject

jlNumeric: (%, PositiveInteger) -> %

from JuliaWSObject

jlRef: % -> SExpression

from JuliaObjectType

jlref: String -> %

from JuliaObjectType

jlSymbolic: % -> String

from JuliaWSObject

jlType: % -> String

from JuliaObjectType

join: (%, %) -> %

from JuliaWSAggregate JuliaWSVector E

jordan: % -> Record(s: %, j: %)

jordan(m) computes the Jordan decomposition of of the square matrix m.

jWSAggregate: List JuliaWSVector E -> %

from JuliaWSAggregate JuliaWSVector E

jWSInterpret: (String, String) -> %

from JuliaWSObject

jWSMatrix: String -> %

jWSMatrix(str) constructs str as a JuliaWSMatrix. str must be in the WS language (WS list of WS list(s)).

kronecker_prod1: (%, Integer, List List NonNegativeInteger, List %, NonNegativeInteger, NonNegativeInteger, Union(E, one)) -> Void

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

kroneckerProduct: (%, %) -> %

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

kroneckerProduct: List % -> %

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

kroneckerSum: (%, %) -> %

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

kroneckerSum: List % -> %

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

last: % -> JuliaWSVector E

from JuliaWSAggregate JuliaWSVector E

latex: % -> String

from SetCategory

length: % -> JuliaWSInteger

from JuliaWSAggregate JuliaWSVector E

less?: (%, NonNegativeInteger) -> Boolean

from Aggregate

linearSolve: (%, %) -> %

linearSolve(mat, b) finds x, solution of the equation mat * x = b.

listOfLists: % -> List List E

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

lu: % -> Record(lu: %, p: %, c: %)

lu(m) computes the lU decomposition of the matrix m.

map!: (E -> E, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

map: ((E, E) -> E, %, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

map: ((E, E) -> E, %, %, E) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

map: (E -> E, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

matrix: (NonNegativeInteger, NonNegativeInteger, (Integer, Integer) -> E) -> %

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

matrix: JuliaWSVector E -> %

matrix(vec) returns vec as a matrix (inplace coercion).

matrix: List List E -> %

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

matrixFunction: (JuliaWSExpression, %) -> JuliaWSMatrix JuliaWSExpression

matrixFunction(func, m) applies the matrix function func, if available, to the matrix m. Note that it is not an element-wise operation. For example: example{m := jWSMatrix(”{{1.2, 1.7},{1.12, -2.1}}”)@JWSMAT(JWSREAL)} example{matrixFunction(“Sqrt”, m)}

max: % -> E if E has OrderedSet

from HomogeneousAggregate E

max: ((E, E) -> Boolean, %) -> E

from HomogeneousAggregate E

maxColIndex: % -> Integer

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

maxRowIndex: % -> Integer

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

member?: (E, %) -> Boolean

from HomogeneousAggregate E

members: % -> List E

from HomogeneousAggregate E

min: % -> E if E has OrderedSet

from HomogeneousAggregate E

minColIndex: % -> Integer

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

minordet: % -> E if E has CommutativeRing

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

minors: % -> %

minors(m) returns the minors of m.

minors: (%, JuliaWSInteger) -> %

minors(m,i) returns the i-th minors of m.

minRowIndex: % -> Integer

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

more?: (%, NonNegativeInteger) -> Boolean

from Aggregate

mutable?: % -> Boolean

from JuliaObjectType

ncols: % -> NonNegativeInteger

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

new: (NonNegativeInteger, NonNegativeInteger, E) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

norm: % -> E

norm(m) returns the norm of m, i.e. the value of the maximum singular values of m.

norm: (%, JuliaWSExpression) -> E

norm(m, type) returns the type norm of m. For example, norm(m,2) returns the usual norm, norm(m, “Infinity”) or norm(m, “Frobenius”) returns their respective norms. See documentation for information.

nothing?: % -> Boolean

from JuliaObjectType

nrows: % -> NonNegativeInteger

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

nullity: % -> NonNegativeInteger if E has IntegralDomain

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

nullSpace: % -> JuliaWSList JuliaWSVector E

nullSpace(m) returns the list of vector

nullSpace: % -> List JuliaWSVector E if E has IntegralDomain

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

part: (%, JuliaWSInteger) -> JuliaWSVector E

from JuliaWSAggregate JuliaWSVector E

parts: % -> List E

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

permanent: % -> E

permanent(m) returns the permanent of m.

Pfaffian: % -> E if E has CommutativeRing

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

positiveDefinite?: % -> Boolean

positiveDefinite?(m) checks whether or not m is positive definite.

positivePower: (%, Integer) -> %

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

prepend: (%, JuliaWSVector E) -> %

from JuliaWSAggregate JuliaWSVector E

qelt: (%, Integer) -> JuliaWSVector E

from JuliaWSAggregate JuliaWSVector E

qelt: (%, Integer, Integer) -> E

qelt(mat, m, n) returns the element (m,n) of the matrix mat. No checks are done at the FriCAS level.

qnew: (NonNegativeInteger, NonNegativeInteger) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

qr: % -> Record(q: %, r: %)

qr(m) computes the QR decomposition of the matrix m.

qsetelt!: (%, Integer, Integer, E) -> E

qsetelt!(mat,n,m,elt) returns matrix mat with element (n,m) replaced by the element elt.

qsetelt!: (%, Integer, JuliaWSVector E) -> %

from JuliaWSAggregate JuliaWSVector E

qsetelt: (%, Integer, Integer, E) -> %

qsetelt(mat,n,m,elt) returns a new matrix with element (n,m) replaced by the element elt.

qsetelt: (%, Integer, JuliaWSVector E) -> %

from JuliaWSAggregate JuliaWSVector E

randomComplexMatrix: (JuliaWSList JuliaWSComplex, JuliaWSList JuliaWSInteger) -> JuliaWSMatrix JuliaWSComplex

randomComplexMatrix(range, dims) returns a random matrix with random complex numbers in the range range and dims dimensions. example{range:=jWSList(”{1+I}”)@JWSLIST(JWSCPLX)} example{randomComplexMatrix(range,jWSList(”{3,3}”)$JWSLIST(JWSINT))@JWSMAT(JWSCPLX)}

randomRealMatrix: (JuliaWSList JuliaWSReal, JuliaWSList JuliaWSInteger) -> JuliaWSMatrix JuliaWSReal

randomRealMatrix(range, dims) returns a random matrix with random numbers in the range range and dims dimensions. example{range := jWSList(”{-5,5}”)$JWSLIST(JWSREAL)} example{randomRealMatrix(range,jWSList(”{3,3}”)$JWSLIST(JWSINT))@JWSMAT(JWSREAL)}

rank: % -> NonNegativeInteger if E has IntegralDomain

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

removeDuplicates: % -> %

from JuliaWSAggregate JuliaWSVector E

replacePart: (%, %) -> %

from JuliaWSAggregate JuliaWSVector E

rest: % -> %

from JuliaWSAggregate JuliaWSVector E

reverse: % -> %

from JuliaWSAggregate JuliaWSVector E

reverse: (%, JuliaWSInteger) -> %

from JuliaWSAggregate JuliaWSVector E

reverse: (%, JuliaWSList JuliaWSInteger) -> %

from JuliaWSAggregate JuliaWSVector E

riffle: (%, %) -> %

from JuliaWSAggregate JuliaWSVector E

riffle: (%, %, %) -> %

from JuliaWSAggregate JuliaWSVector E

row: (%, Integer) -> %

row(mat,i) returns the i-th row.

row: (%, Integer) -> JuliaWSVector E

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

rowEchelon: % -> % if E has EuclideanDomain

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

rowSlice: % -> Segment Integer

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

sample: %

from Aggregate

scalarMatrix: (NonNegativeInteger, E) -> %

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

schur: % -> Record(q: %, t: %)

schurm) computes the Schur decomposition of of the square matrix m.

setColumn!: (%, Integer, JuliaWSVector E) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

setelt!: (%, Integer, Integer, E) -> E

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

setelt!: (%, Integer, JuliaWSVector E) -> %

from JuliaWSAggregate JuliaWSVector E

setelt!: (%, Integer, List Integer, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

setelt!: (%, Integer, List Segment Integer, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

setelt!: (%, List Integer, Integer, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

setelt!: (%, List Integer, List Integer, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

setelt!: (%, List Integer, Segment Integer, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

setelt!: (%, List Segment Integer, Integer, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

setelt!: (%, List Segment Integer, List Segment Integer, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

setelt!: (%, List Segment Integer, Segment Integer, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

setelt!: (%, Segment Integer, List Integer, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

setelt!: (%, Segment Integer, List Segment Integer, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

setelt!: (%, Segment Integer, Segment Integer, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

setelt: (%, Integer, Integer, E) -> %

setelt(mat,n,m,elt) returns a new matrix with element (n,m) replaced by the element elt.

setelt: (%, Integer, JuliaWSVector E) -> %

from JuliaWSAggregate JuliaWSVector E

setIntersection: (%, %) -> %

from JuliaWSAggregate JuliaWSVector E

setRow!: (%, Integer, JuliaWSVector E) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

setsubMatrix!: (%, Integer, Integer, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

size?: (%, NonNegativeInteger) -> Boolean

from Aggregate

smaller?: (%, %) -> Boolean if E has Comparable

from Comparable

sort: % -> %

from JuliaWSAggregate JuliaWSVector E

sorted?: % -> Boolean

from JuliaWSAggregate JuliaWSVector E

square?: % -> Boolean

square?(m) returns true if m is a square matrix (i.e. if m has the same number of rows as columns) and false otherwise.

squareTop: % -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

string: % -> String

from JuliaObjectType

subMatrix: (%, Integer, Integer, Integer, Integer) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

svd: % -> Record(S: %, sv: %, V: %)

svd(m) computes the singular value decomposition of the matrix m.

svdvals: % -> JuliaWSList E

svdvals(m) returns the singular values of the matrix m.

swapColumns!: (%, Integer, Integer) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

swapRows!: (%, Integer, Integer) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

symmetric?: % -> Boolean

symmetric?(m) returns true if the matrix m is square and symmetric (i.e. m[i, j] = m[j, i] for all i and j) and false otherwise.

take: (%, Integer) -> %

from JuliaWSAggregate JuliaWSVector E

take: (%, JuliaWSList JuliaWSInteger) -> %

from JuliaWSAggregate JuliaWSVector E

toString: % -> String

from JuliaWSObject

toString: (%, JuliaWSExpression) -> String

toString(mat, form) returns the string representation of mat with WS language format form.

total: % -> JuliaWSVector E if JuliaWSVector E has JuliaWSNumber

from JuliaWSAggregate JuliaWSVector E

trace: % -> E

trace(m) returns the trace of m.

transpose: % -> %

transpose(m) returns the tranposition of m.

transpose: JuliaWSVector E -> %

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

union: (%, %) -> %

from JuliaWSAggregate JuliaWSVector E

vertConcat: (%, %) -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

vertConcat: List % -> %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

vertSplit: (%, List NonNegativeInteger) -> List %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

vertSplit: (%, PositiveInteger) -> List %

from TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)

zero?: % -> Boolean

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

zero: (NonNegativeInteger, NonNegativeInteger) -> %

from MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

Aggregate

BasicType

CoercibleTo OutputForm

Comparable if E has Comparable

ConvertibleTo String

Evalable E if E has Evalable E

finiteAggregate

Hashable if E has Hashable

HomogeneousAggregate E

InnerEvalable(E, E) if E has Evalable E

JuliaObjectType

JuliaType

JuliaWSAggregate JuliaWSVector E

JuliaWSObject

MatrixCategory(E, JuliaWSVector E, JuliaWSVector E)

SetCategory

shallowlyMutable

TwoDimensionalArrayCategory(E, JuliaWSVector E, JuliaWSVector E)