Matrix -- the class of all matrices

Functions and methods returning a matrix:

• Matrix + Matrix -- see + -- a unary or binary operator, usually used for addition
• - Matrix -- see - -- a unary or binary operator, usually used for negation or subtraction
• Matrix - Matrix -- see - -- a unary or binary operator, usually used for negation or subtraction
• adjoint'(Matrix,Module,Module) -- see adjoint -- the tensor-Hom adjunction maps
• adjoint(Matrix,Module,Module) -- see adjoint -- the tensor-Hom adjunction maps
• ambient(Matrix) -- get the map between the ambient free modules
• basis -- basis or generating set of all or part of a ring, ideal or module
• basis(List,RingMap) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• basis(RingMap) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• basis(Sequence,RingMap) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,RingMap) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• borel(Matrix) -- make a Borel fixed submodule
• complement(Matrix) -- see complement -- find the minimal generators for cokernel of a matrix (low level form)
• compose(Module,Module,Module) -- see compose -- composition as a pairing on Hom-modules
• compress(Matrix) -- see compress -- extract nonzero columns from a matrix
• contract'(Matrix,Matrix) -- contract a matrix by a matrix, the dual notion
• contract(Matrix,Matrix) -- contract a matrix by a matrix
• cover(Matrix) -- get the map between the covering free modules
• coverMap(Module) -- the surjective map from a free module to a module corresponding to the generators
• diagonalMatrix -- make a diagonal matrix
• diff'(Matrix,Matrix) -- differentiate a matrix by a matrix, the dual notion
• diff(Matrix,Matrix) -- differentiate a matrix by a matrix
• divideByVariable(Matrix,RingElement) -- see divideByVariable -- divide all columns by a (power of a) variable
• divideByVariable(Matrix,RingElement,ZZ) -- see divideByVariable -- divide all columns by a (power of a) variable
• dual(Matrix) -- dual of a map
• Ext^ZZ(Matrix,Ideal) -- see Ext^ZZ(Matrix,Module) -- map between Ext modules
• Ext^ZZ(Matrix,Module) -- map between Ext modules
• Ext^ZZ(Matrix,Ring) -- see Ext^ZZ(Matrix,Module) -- map between Ext modules
• Ext^ZZ(Ideal,Matrix) -- see Ext^ZZ(Module,Matrix) -- map between Ext modules
• Ext^ZZ(Module,Matrix) -- map between Ext modules
• Ext^ZZ(Ring,Matrix) -- see Ext^ZZ(Module,Matrix) -- map between Ext modules
• exteriorPower(ZZ,Matrix) -- exterior power of a matrix
• flatten(Matrix) -- see flatten -- flatten a nested list or a matrix
• flip(Module,Module) -- see flip -- isomorphism map of commutativity of tensor product
• generators(GroebnerBasis) -- the generator matrix of a Gröbner basis
• generators(Ideal) -- the generator matrix of an ideal
• generators(Module) -- the generator matrix of a module
• genericMatrix -- make a generic matrix of variables
• genericSkewMatrix -- make a generic skew symmetric matrix of variables
• genericSymmetricMatrix -- make a generic symmetric matrix
• getChangeMatrix(GroebnerBasis) -- see getChangeMatrix -- get the change of basis matrix
• groebnerBasis -- Gröbner basis, as a matrix
• Hom(Matrix,Matrix) -- see Hom(Module,Matrix) -- induced map on Hom
• Hom(Matrix,Module) -- see Hom(Module,Matrix) -- induced map on Hom
• Hom(Module,Matrix) -- induced map on Hom
• homogenize(Matrix,RingElement) -- see homogenize -- homogenize with respect to a variable
• homogenize(Matrix,RingElement,List) -- see homogenize -- homogenize with respect to a variable
• homogenize(RingElement,RingElement) -- see homogenize -- homogenize with respect to a variable
• homomorphism'(Matrix) -- see homomorphism' -- get the element of Hom from a homomorphism
• inducedMap(Module,Module) -- compute the map induced by the identity
• inducedMap(Module,Module,Matrix) -- compute the induced map
• inducedMap(Module,Nothing,Matrix) -- see inducedMap(Module,Module,Matrix) -- compute the induced map
• jacobian(Ideal) -- the Jacobian matrix of the generators of an ideal
• jacobian(Matrix) -- the matrix of partial derivatives of polynomials in a matrix
• jacobian(RingElement) -- see jacobian(Matrix) -- the matrix of partial derivatives of polynomials in a matrix
• jacobian(Ring) -- the Jacobian matrix of the polynomials defining a quotient ring
• koszul(ZZ,Matrix) -- a differential in a Koszul complex
• leadTerm(GroebnerBasis) -- see leadTerm(Matrix) -- get the greatest term of each column
• leadTerm(Matrix) -- get the greatest term of each column
• leadTerm(ZZ,Ideal) -- get the ideal of lead polynomials
• leadTerm(ZZ,GroebnerBasis) -- see leadTerm(ZZ,Matrix) -- get the matrix of lead polynomials of each column
• leadTerm(ZZ,Matrix) -- get the matrix of lead polynomials of each column
• lift(Matrix,type of Number) -- see lift -- lift to another ring
• lift(Matrix,type of RingElement) -- see lift -- lift to another ring
• lift(MutableMatrix,type of RingElement) -- see lift -- lift to another ring
• map(Matrix) -- make a matrix with a different degree
• map(Module) -- identity map
• map(Module,Module,Function) -- create a matrix by specifying a function that gives each entry
• map(Module,Module,List) -- create a matrix by giving a sparse or dense list of entries
• map(Module,Module,Matrix) -- create the matrix induced on generators by a given matrix
• map(Module,Module,Number) -- see map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators
• map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators
• map(Module,Module,ZZ) -- see map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators
• map(Module,ZZ,ZZ) -- see map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators
• map(Module,Module,RingMap,List) -- see map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
• map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
• map(Module,Nothing,RingMap,List) -- see map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
• map(Module,Nothing,RingMap,Matrix) -- see map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
• map(Module,RingMap) -- see map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
• map(Module,Nothing,List) -- create a matrix by giving a doubly nested list of ring elements
• map(Module,Nothing,Matrix) -- recast a matrix to have a new target, and a free module as source
• map(Module,ZZ,Function) -- create a matrix from a free module by specifying a function that gives each entry
• map(Module,ZZ,List) -- create a matrix by giving a sparse or dense list of entries
• Matrix % GroebnerBasis -- compute the normal form of a ring element or matrix using a Gröbner basis
• Matrix * Matrix -- matrix multiplication
• Matrix ** Ring -- tensor product
• Ring ** Matrix -- see Matrix ** Ring -- tensor product
• Matrix ++ Matrix -- direct sum of maps
• Matrix ++ RingElement -- see Matrix ++ Matrix -- direct sum of maps
• RingElement ++ Matrix -- see Matrix ++ Matrix -- direct sum of maps
• RingElement ++ RingElement -- see Matrix ++ Matrix -- direct sum of maps
• Matrix ^ Array -- component of map corresponding to summand of target
• Matrix ^ List -- select rows
• MutableMatrix ^ List -- see Matrix ^ List -- select rows
• Matrix ^ ZZ -- power
• Matrix ^** ZZ (missing documentation)
• Matrix _ Array -- component of map corresponding to summand of source
• Matrix _ List -- select columns
• MutableMatrix _ List -- see Matrix _ List -- select columns
• Matrix | Matrix -- join matrices horizontally
• RingElement | RingElement -- see Matrix | Matrix -- join matrices horizontally
• Matrix || Matrix -- join matrices vertically
• RingElement || RingElement -- see Matrix || Matrix -- join matrices vertically
• matrix(List) -- create a matrix from a doubly-nested list of ring elements or matrices
• matrix(Matrix) -- the matrix between generators
• matrix(Ring,List) -- create a matrix from a doubly nested list of ring elements or matrices
• matrix(RingFamily,List) -- see matrix(Ring,List) -- create a matrix from a doubly nested list of ring elements or matrices
• matrix(String) (missing documentation)
• Matrix % Ideal -- see methods for normal forms and remainder -- normal form of ring elements and matrices
• Matrix % Matrix -- see methods for normal forms and remainder -- normal form of ring elements and matrices
• Matrix % Module -- see methods for normal forms and remainder -- normal form of ring elements and matrices
• Matrix % MonomialIdeal -- see methods for normal forms and remainder -- normal form of ring elements and matrices
• mingens(GroebnerBasis) -- (partially constructed) minimal generator matrix
• mingens(Ideal) -- see mingens(Module) -- minimal generator matrix
• mingens(Module) -- minimal generator matrix
• minimalPresentation(Matrix) -- minimally present source and target of a matrix
• prune(Matrix) -- see minimalPresentation(Matrix) -- minimally present source and target of a matrix
• Module ^ Array -- projection onto summand
• Module ^ List -- projection onto summand
• Module _ Array -- inclusion from summand
• Module _ List -- map from free module to some generators
• modulo(Matrix,Matrix) -- see modulo -- find the pre-image (pullback) of image of a map (low level version)
• modulo(Matrix,Nothing) -- see modulo -- find the pre-image (pullback) of image of a map (low level version)
• modulo(Nothing,Matrix) -- see modulo -- find the pre-image (pullback) of image of a map (low level version)
• part(List,Matrix) (missing documentation)
• part(Sequence,RingMap) (missing documentation)
• part(ZZ,Matrix) (missing documentation)
• presentation(Module) -- presentation of a module
• presentation(QuotientRing) -- see presentation(PolynomialRing,QuotientRing) -- presentation of a quotient ring
• Matrix \\ Matrix -- see quotient' -- factor a map through another with the same source
• quotient'(Matrix,Matrix) -- see quotient' -- factor a map through another with the same source
• Matrix // GroebnerBasis -- see quotient(Matrix,Matrix) -- factor a map through another with the same target
• Matrix // Matrix -- see quotient(Matrix,Matrix) -- factor a map through another with the same target
• Matrix // MonomialIdeal -- see quotient(Matrix,Matrix) -- factor a map through another with the same target
• Matrix // Number -- see quotient(Matrix,Matrix) -- factor a map through another with the same target
• Matrix // RingElement -- see quotient(Matrix,Matrix) -- factor a map through another with the same target
• Number // Matrix -- see quotient(Matrix,Matrix) -- factor a map through another with the same target
• quotient(Matrix,GroebnerBasis) -- see quotient(Matrix,Matrix) -- factor a map through another with the same target
• quotient(Matrix,Matrix) -- factor a map through another with the same target
• RingElement // GroebnerBasis -- see quotient(Matrix,Matrix) -- factor a map through another with the same target
• RingElement // Matrix -- see quotient(Matrix,Matrix) -- factor a map through another with the same target
• quotientRemainder(Matrix,GroebnerBasis) -- see quotientRemainder -- matrix quotient and remainder
• quotientRemainder(Matrix,Matrix) -- see quotientRemainder -- matrix quotient and remainder
• quotientRemainder'(Matrix,Matrix) -- see quotientRemainder' -- matrix quotient and remainder (opposite)
• random(Module,Module) -- get a random map of module
• rays(Matrix)
• relations(Module) -- see relations -- the defining relations
• remainder(Matrix,GroebnerBasis) -- see remainder -- matrix remainder
• remainder(Matrix,Matrix) -- see remainder -- matrix remainder
• remainder'(Matrix,Matrix) -- see remainder' -- matrix remainder (opposite)
• reshape(Module,Module,Matrix) -- see reshape -- reshape a matrix
• RingMap Matrix -- see RingMap RingElement -- apply a ring map
• schreyerOrder(Matrix) -- create a matrix with the same entries whose source free module has a Schreyer monomial order
• schreyerOrder(Module) -- obtain Schreyer order information
• selectInSubring(ZZ,Matrix) -- see selectInSubring -- select columns in a subring
• submatrix -- select part of a matrix
• submatrix' -- exclude rows and/or columns of a matrix
• substitute(Matrix,List) -- see substitute -- substituting values for variables
• substitute(Matrix,Matrix) -- see substitute -- substituting values for variables
• substitute(Matrix,Ring) -- see substitute -- substituting values for variables
• substitute(Matrix,RingFamily) -- see substitute -- substituting values for variables
• substitute(Matrix,ZZ) -- see substitute -- substituting values for variables
• super(Matrix) -- see super -- get the ambient module
• symmetricPower(ZZ,Matrix) -- see symmetricPower -- symmetric power
• syz -- the syzygy matrix
• syz(GroebnerBasis) -- retrieve the syzygy matrix
• syz(Matrix) -- compute the syzygy matrix
• Matrix ** Matrix -- see tensor(Matrix,Matrix) -- tensor product
• tensor(Matrix,Matrix) -- tensor product
• Matrix ** Module -- see tensor(Matrix,Module) -- tensor product
• Module ** Matrix -- see tensor(Matrix,Module) -- tensor product
• tensor(Matrix,Module) -- tensor product
• tensor(Module,Matrix) -- see tensor(Matrix,Module) -- tensor product
• RingMap ** Matrix -- see tensor(RingMap,Matrix) -- tensor product via a ring map
• tensor(RingMap,Matrix) -- tensor product via a ring map
• tensorAssociativity(Module,Module,Module) -- see tensorAssociativity -- associativity isomorphisms for tensor products
• transpose(Matrix) -- see transpose -- transpose a matrix or table
• truncate(List,List,Matrix) (missing documentation)
• truncate(List,Matrix)
• truncate(Nothing,List,Matrix) (missing documentation)
• truncate(Nothing,ZZ,Matrix) (missing documentation)
• truncate(ZZ,ZZ,Matrix) (missing documentation)
• vars(Ring) -- row matrix of the variables
• wedgeProduct(ZZ,ZZ,Module) -- the exterior multiplication map

Methods that use a matrix:

• Matrix * Number -- see * -- a binary operator, usually used for multiplication
• Matrix * RingElement -- see * -- a binary operator, usually used for multiplication
• Matrix * Vector -- see * -- a binary operator, usually used for multiplication
• Number * Matrix -- see * -- a binary operator, usually used for multiplication
• RingElement * Matrix -- see * -- a binary operator, usually used for multiplication
• Matrix + Number -- see + -- a unary or binary operator, usually used for addition
• Matrix + RingElement -- see + -- a unary or binary operator, usually used for addition
• Number + Matrix -- see + -- a unary or binary operator, usually used for addition
• RingElement + Matrix -- see + -- a unary or binary operator, usually used for addition
• Matrix - Number -- see - -- a unary or binary operator, usually used for negation or subtraction
• Matrix - RingElement -- see - -- a unary or binary operator, usually used for negation or subtraction
• Number - Matrix -- see - -- a unary or binary operator, usually used for negation or subtraction
• RingElement - Matrix -- see - -- a unary or binary operator, usually used for negation or subtraction
• Matrix == Matrix -- see basic arithmetic of matrices
• basis(InfiniteNumber,InfiniteNumber,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• basis(InfiniteNumber,List,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• basis(InfiniteNumber,ZZ,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• basis(List,InfiniteNumber,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• basis(List,List,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• basis(List,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• basis(List,ZZ,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• basis(Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,InfiniteNumber,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,List,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• basis(ZZ,ZZ,Matrix) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• betti(Matrix) -- see betti -- display or modify a Betti diagram
• clean(RR,Matrix) -- see clean -- set to zero elements that are approximately zero
• coefficients(Matrix) -- see coefficients -- get the monomials and coefficients of a polynomial or matrix
• coimage(Matrix) -- see coimage -- coimage of a map
• cokernel(Matrix) -- cokernel of a map of modules
• components(Matrix) -- see components -- list the components of a direct sum
• contract(Matrix,Number) -- see contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(Matrix,RingElement) -- see contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(Matrix,Vector) -- see contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(Number,Matrix) -- see contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(RingElement,Matrix) -- see contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(Vector,Matrix) -- see contract(Matrix,Matrix) -- contract a matrix by a matrix
• degree(Matrix) (missing documentation)
• degrees(Matrix) -- degrees of target and source
• describe(Matrix) -- see describe -- real description
• determinant(Matrix) -- see determinant -- determinant of a matrix
• diagonalMatrix(Matrix) -- make a diagonal matrix from entries of a matrix
• diff(Matrix,Vector) -- see diff(Matrix,Matrix) -- differentiate a matrix by a matrix
• diff(Vector,Matrix) -- see diff(Matrix,Matrix) -- differentiate a matrix by a matrix
• diff(Matrix,RingElement) -- differentiation
• diff(RingElement,Matrix) -- differentiate each entry of a matrix
• directSum(Matrix) -- see directSum -- direct sum of modules or maps
• eagonNorthcott(Matrix) -- see eagonNorthcott -- Eagon-Northcott complex of a matrix of linear forms
• eigenvalues(Matrix) -- see eigenvalues -- find eigenvalues of a matrix
• eigenvectors(Matrix) -- see eigenvectors -- find eigenvectors of a matrix over real or complex numbers
• entries(Matrix) -- see entries -- get the entries of a matrix
• fittingIdeal(ZZ,Matrix) -- see fittingIdeal -- Fitting ideal of a module
• forceGB(Matrix) -- see forceGB -- declare that the columns of a matrix are a Gröbner basis
• gb(Matrix) -- see gb -- compute a Gröbner basis
• gbRemove(Matrix) -- see gbRemove -- remove Gröbner basis
• gbSnapshot(Matrix) -- see gbSnapshot -- the Gröbner basis matrix as so far computed
• Matrix _ ZZ -- see generators of rings, ideals, and modules
• groebnerBasis(Matrix) -- see groebnerBasis -- Gröbner basis, as a matrix
• homology(Matrix,Matrix) -- homology of a pair of maps
• homomorphism(Matrix) -- see homomorphism -- get the homomorphism from element of Hom
• ideal(Matrix) -- make an ideal
• image(Matrix) -- image of a map
• indices(Matrix) -- see indices(RingElement) -- indices of variables occurring in a polynomial
• inducedMap(Nothing,Module,Matrix) -- see inducedMap(Module,Module,Matrix) -- compute the induced map
• inducedMap(Nothing,Nothing,Matrix) -- see inducedMap(Module,Module,Matrix) -- compute the induced map
• inducesWellDefinedMap(Module,Module,Matrix) -- see inducesWellDefinedMap -- whether a map is well defined
• inducesWellDefinedMap(Module,Nothing,Matrix) -- see inducesWellDefinedMap -- whether a map is well defined
• inducesWellDefinedMap(Nothing,Module,Matrix) -- see inducesWellDefinedMap -- whether a map is well defined
• inducesWellDefinedMap(Nothing,Nothing,Matrix) -- see inducesWellDefinedMap -- whether a map is well defined
• installHilbertFunction(Matrix,RingElement) (missing documentation)
• intersect(Matrix)
• intersect(Matrix,Matrix)
• intersect(Matrix,Matrix,Matrix,Matrix)
• inverse(Matrix) -- compute the inverse
• isHomogeneous(Matrix) -- see isHomogeneous -- whether something is homogeneous (graded)
• isInjective(Matrix) -- see isInjective -- whether a map is injective
• isIsomorphism(Matrix) -- see isIsomorphism -- whether a map is an isomorphism
• isSurjective(Matrix) -- see isSurjective -- whether a map is surjective
• isWellDefined(Matrix) -- see isWellDefined -- whether a map is well defined
• kernel(Matrix) -- kernel of a matrix
• koszul(Matrix) -- the Koszul complex
• leadComponent(Matrix) -- see leadComponent -- the leading component(s) of a vector or matrix
• lift(Matrix,type of CC_*,type of QQ) -- see lift -- lift to another ring
• lift(Matrix,type of CC_*,type of RR_*) -- see lift -- lift to another ring
• lift(Matrix,type of CC_*,type of ZZ) -- see lift -- lift to another ring
• lift(Matrix,type of QQ,type of QQ) -- see lift -- lift to another ring
• lift(Matrix,type of QQ,type of ZZ) -- see lift -- lift to another ring
• lift(Matrix,type of RR_*,type of QQ) -- see lift -- lift to another ring
• lift(Matrix,type of RR_*,type of ZZ) -- see lift -- lift to another ring
• lift(Matrix,type of RRi_*,type of QQ) -- see lift -- lift to another ring
• lift(Matrix,type of RRi_*,type of RR_*) -- see lift -- lift to another ring
• lift(Matrix,type of RRi_*,type of ZZ) -- see lift -- lift to another ring
• lift(Matrix,type of ZZ,type of ZZ) -- see lift -- lift to another ring
• LUdecomposition(Matrix) -- see LUdecomposition -- compute the LU decomposition of a matrix
• map(Ring,Matrix) -- make a ring map
• map(Ring,Ring,Matrix) -- make a ring map
• markedGB(Matrix,Matrix) -- make a marked Gröbner basis
• Matrix ** RingElement
• Matrix / Number -- scalar division
• Matrix / RingElement -- see Matrix / Number -- scalar division
• Matrix ^~ (missing documentation)
• Matrix _ Sequence -- get entry of matrix
• Matrix | Number -- see Matrix | Matrix -- join matrices horizontally
• Matrix | RingElement -- see Matrix | Matrix -- join matrices horizontally
• Number | Matrix -- see Matrix | Matrix -- join matrices horizontally
• RingElement | Matrix -- see Matrix | Matrix -- join matrices horizontally
• Matrix || Number -- see Matrix || Matrix -- join matrices vertically
• Matrix || RingElement -- see Matrix || Matrix -- join matrices vertically
• Number || Matrix -- see Matrix || Matrix -- join matrices vertically
• RingElement || Matrix -- see Matrix || Matrix -- join matrices vertically
• Matrix Vector (missing documentation)
• Matrix % RingElement -- see methods for normal forms and remainder -- normal form of ring elements and matrices
• RingElement % Matrix -- see methods for normal forms and remainder -- normal form of ring elements and matrices
• minors(ZZ,Matrix) -- ideal generated by minors
• monomialIdeal(Matrix) -- monomial ideal of lead monomials
• monomials(Matrix) -- see monomials -- matrix of monomials in a ring element or matrix
• mutableMatrix(Matrix) -- see mutableMatrix -- make a mutable matrix
• newCoordinateSystem(PolynomialRing,Matrix) -- see newCoordinateSystem -- change variables
• norm(InfiniteNumber,Matrix) -- see norm
• norm(Matrix) -- see norm
• norm(RR,Matrix) -- see norm
• numColumns(Matrix) -- number of columns in a matrix or mutable matrix
• numeric(Matrix) -- see numeric -- convert to floating point
• numeric(ZZ,Matrix) -- see numeric -- convert to floating point
• numRows(Matrix) -- number of rows in a matrix or mutable matrix
• permanents(ZZ,Matrix) -- see permanents -- ideal generated by square permanents of a matrix
• pfaffians(ZZ,Matrix) -- see pfaffians -- ideal generated by Pfaffians
• pivots(Matrix) -- list of pivot locations of a matrix
• precision(Matrix) -- see precision
• preimage(Matrix,Module) -- see preimage -- preimage of a map
• pullback(Matrix,Matrix) (missing documentation)
• pushout(Matrix,Matrix) (missing documentation)
• QRDecomposition(Matrix) -- see QRDecomposition -- compute a QR decomposition of a real matrix
• rank(Matrix) -- see rank -- compute the rank
• reducedRowEchelonForm(Matrix) -- see reducedRowEchelonForm -- compute the reduced row echelon form of a matrix or mutable matrix over a field
• ring(Matrix) -- see ring -- get the associated ring of an object
• rsort(Matrix) -- see rsort -- sort a list or matrix in reverse order
• smithNormalForm(Matrix) -- smith normal form for a matrix over a PID
• solve(Matrix,Matrix) -- see solve -- solve linear equation(s)
• solve(Matrix,Vector) (missing documentation)
• sort(Matrix) -- sort the columns of a matrix
• sortColumns(Matrix) -- see sortColumns -- permutation giving sort order
• source(Matrix) -- find the source module of matrix
• submatrix(Matrix,VisibleList,VisibleList) -- see submatrix -- select part of a matrix
• submatrix'(Matrix,Nothing,Nothing) -- see submatrix' -- exclude rows and/or columns of a matrix
• submatrix'(Matrix,Nothing,VisibleList) -- see submatrix' -- exclude rows and/or columns of a matrix
• submatrix'(Matrix,VisibleList) -- see submatrix' -- exclude rows and/or columns of a matrix
• submatrix'(Matrix,VisibleList,Nothing) -- see submatrix' -- exclude rows and/or columns of a matrix
• submatrix'(Matrix,VisibleList,VisibleList) -- see submatrix' -- exclude rows and/or columns of a matrix
• submatrix(Matrix,VisibleList) -- select columns
• submatrixByDegrees(Matrix,List,List) -- see submatrixByDegrees -- submatrix consisting of rows and columns in an interval or box of degrees
• submatrixByDegrees(Matrix,Sequence,Sequence) -- see submatrixByDegrees -- submatrix consisting of rows and columns in an interval or box of degrees
• submatrixByDegrees(Matrix,ZZ,ZZ) -- see submatrixByDegrees -- submatrix consisting of rows and columns in an interval or box of degrees
• subquotient(Matrix,Matrix) -- see subquotient -- make a subquotient module
• subquotient(Matrix,Nothing) -- see subquotient -- make a subquotient module
• subquotient(Module,Matrix,Matrix) -- see subquotient -- make a subquotient module
• subquotient(Module,Matrix,Nothing) -- see subquotient -- make a subquotient module
• subquotient(Module,Nothing,Matrix) -- see subquotient -- make a subquotient module
• subquotient(Nothing,Matrix) -- see subquotient -- make a subquotient module
• substitute(Ideal,Matrix) -- see substitute -- substituting values for variables
• substitute(Matrix,Option) -- see substitute -- substituting values for variables
• substitute(Module,Matrix) -- see substitute -- substituting values for variables
• substitute(RingElement,Matrix) -- see substitute -- substituting values for variables
• substitute(Vector,Matrix) -- see substitute -- substituting values for variables
• support(Matrix) -- see support -- list of variables occurring in a polynomial or matrix
• SVD(Matrix) -- see SVD -- singular value decomposition of a matrix
• symmetricAlgebra(Matrix) -- see symmetricAlgebra -- the symmetric algebra of a module
• symmetricAlgebra(Nothing,Nothing,Matrix) -- see symmetricAlgebra -- the symmetric algebra of a module
• symmetricAlgebra(Nothing,Ring,Matrix) -- see symmetricAlgebra -- the symmetric algebra of a module
• symmetricAlgebra(Ring,Nothing,Matrix) -- see symmetricAlgebra -- the symmetric algebra of a module
• symmetricAlgebra(Ring,Ring,Matrix) -- see symmetricAlgebra -- the symmetric algebra of a module
• target(Matrix) -- find the target module of matrix
• topCoefficients(Matrix) -- see topCoefficients -- first variable and its coefficient of a polynomial or matrix
• trace(Matrix) -- trace of a matrix
• truncate(InfiniteNumber,InfiniteNumber,Matrix) (missing documentation)
• truncate(Nothing,InfiniteNumber,Matrix) (missing documentation)
• truncate(ZZ,Matrix)
• vector(Matrix) -- see vector -- make a vector
• vector(Module,Matrix) -- see vector -- make a vector
• vector(Ring,Matrix) -- see vector -- make a vector
• vector(RingFamily,Matrix) -- see vector -- make a vector

For the programmer

The object Matrix is a type, with ancestor classes HashTable < Thing.

The source of this document is in Macaulay2Doc/doc_matrices.m2:104:0.