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) -- an adjoint map
• adjoint(Matrix,Module,Module) -- an adjoint map
• ambient(Matrix)
• basis -- basis or generating set of all or part of a ring, ideal or module
• borel(Matrix) -- make a Borel fixed submodule
• ChainComplexMap _ ZZ -- component map
• "GradedModuleMap _ ZZ" -- see ChainComplexMap _ ZZ -- component map
• complement(Matrix) -- find the minimal generators for cokernel of a matrix (low level form)
• compose(Module,Module,Module) -- 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 covering free module
• 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,Module) -- map between Ext modules
• 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) -- matrix 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
• HH^ZZ ChainComplexMap -- cohomology of a chain complex map
• HH_ZZ ChainComplexMap -- homology of a chain complex map
• Hom(Matrix,Matrix) -- induced map on Hom
• Hom(Matrix,Module) -- 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 homomorphism from element of Hom
• "homomorphism'(Matrix)" -- see homomorphism' -- get the element of Hom from a homomorphism
• "icFractions(Ring)" -- see icFractions -- fractions integral over an affine domain
• inducedMap(Module,Module) -- compute the map induced by the identity
• inducedMap(Module,Module,Matrix) -- compute the induced map
• jacobian(Ideal) -- the Jacobian matrix of the generators of an ideal
• "jacobian(MonomialIdeal)" -- see jacobian(Ideal) -- the Jacobian matrix of the generators of an ideal
• jacobian(Matrix) -- the matrix of partial derivatives of polynomials in a matrix
• jacobian(Ring) -- the Jacobian matrix of the polynomials defining a quotient ring
• jacobian(RingElement) (missing documentation)
• koszul(ZZ,Matrix) -- a differential in a Koszul complex
• leadTerm(Ideal) -- get the ideal of greatest terms
• "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,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 InexactNumber') (missing documentation)
• lift(MutableMatrix,type of Number) (missing documentation)
• lift(MutableMatrix,type of RingElement) (missing documentation)
• 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 -- calculate the normal form of ring elements and matrices using a (partially computed) Gröbner basis
• Matrix * Matrix -- matrix multiplication
• Matrix ** Matrix -- tensor product
• Matrix ** Module -- tensor product
• "Module ** Matrix" -- see Matrix ** Module -- tensor product
• 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 // GroebnerBasis" -- see Matrix // Matrix -- factor a map through another
• Matrix // Matrix -- factor a map through another
• "Matrix // MonomialIdeal" -- see Matrix // Matrix -- factor a map through another
• "RingElement // GroebnerBasis" -- see Matrix // Matrix -- factor a map through another
• Matrix ^ Array -- component of map corresponding to summand of target
• Matrix ^ List -- select rows
• Matrix ^ ZZ -- power
• Matrix _ Array -- component of map corresponding to summand of source
• 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) -- make a matrix using classic Macaulay syntax
• "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) -- find the pre-image (pullback) of image of a map (low level version)
• "modulo(Matrix,Nothing)" -- see modulo(Matrix,Matrix) -- find the pre-image (pullback) of image of a map (low level version)
• "modulo(Nothing,Matrix)" -- see modulo(Matrix,Matrix) -- find the pre-image (pullback) of image of a map (low level version)
• MutableMatrix ^ List (missing documentation)
• MutableMatrix _ List (missing documentation)
• presentation(Module) -- presentation of a module
• "presentation(QuotientRing)" -- see presentation(PolynomialRing,QuotientRing) -- presentation of a quotient ring
• "quotient'(Matrix,Matrix)" -- see quotient' -- matrix quotient (opposite)
• quotient(Matrix,GroebnerBasis) -- matrix quotient
• "quotient(Matrix,Matrix)" -- see quotient(Matrix,GroebnerBasis) -- matrix quotient
• "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) -- make a random module map
• "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 quotient and remainder (opposite)
• reshape(Module,Module,Matrix) -- 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
• 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
• sum(ChainComplexMap) -- direct sum of the components of a chain map
• "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
• tensor(Matrix,Matrix) (missing documentation)
• "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
• "toDual(ZZ,Ideal)" -- see toDual -- finds the inverse system to an ideal up to a given degree
• "toDual(ZZ,Matrix)" -- see toDual -- finds the inverse system to an ideal up to a given degree
• transpose(Matrix) -- transpose a matrix
• vars(Ring) -- row matrix of the variables
• "versalEmbedding(Ideal)" -- see versalEmbedding -- Compute a versal embedding
• "versalEmbedding(Module)" -- see versalEmbedding -- Compute a versal embedding
• 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 // Number" -- see // -- a binary operator, usually used for quotient
• "Number // Matrix" -- see // -- a binary operator, usually used for quotient
• "Matrix == Matrix" -- see == -- equality
• "Matrix == Number" -- see == -- equality
• "Matrix == RingElement" -- see == -- equality
• "Matrix == ZZ" -- see == -- equality
• "Number == Matrix" -- see == -- equality
• "RingElement == Matrix" -- see == -- equality
• "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(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
• chainComplex(Matrix) -- make a small chain complex
• "checkDegrees(Matrix,Matrix)" -- see checkDegrees -- compares the degrees of generators of two modules
• "clean(RR,Matrix)" -- see clean -- Set to zero elements that are approximately zero
• "coefficients(Matrix)" -- see coefficients -- monomials and their coefficients
• "coimage(Matrix)" -- see coimage -- coimage of a map
• "cokernel(Matrix)" -- see cokernel -- cokernel of a map of modules, graded modules, or chaincomplexes
• "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) -- 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 RR or CC
• "entries(Matrix)" -- see entries -- lists the entries of a matrix
• "Ext^ZZ(Matrix,Ideal)" -- see 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
• extend(ChainComplex,ChainComplex,Matrix) -- extend a module map to a chain map, if possible
• fittingIdeal(ZZ,Matrix) (missing documentation)
• "forceGB(Matrix)" -- see forceGB -- declare that the columns of a matrix are a Gröbner basis
• "fromDividedPowers(Matrix)" -- see fromDividedPowers -- Translates from divided power monomial basis to ordinary monomial basis
• "fromDual(Matrix)" -- see fromDual -- Ideal from inverse system
• "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 ideals and modules
• "gradedModuleMap(Matrix)" -- see gradedModuleMap -- make a map of graded modules
• gramm(Matrix) (missing documentation)
• "groebnerBasis(Matrix)" -- see groebnerBasis -- Gröbner basis, as a matrix
• hermite(Matrix) (missing documentation)
• homology(Matrix,Matrix) -- homology of a pair of maps
• ideal(Matrix) -- make an ideal
• "image(Matrix)" -- see image -- image of a map
• "indices(Matrix)" -- see indices(RingElement) -- indices of variables occurring in a polynomial
• "inducedMap(Module,Nothing,Matrix)" -- see inducedMap(Module,Module,Matrix) -- compute the induced map
• "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
• InfiniteNumber * Matrix (missing documentation)
• installHilbertFunction(Matrix,RingElement) (missing documentation)
• inverse(Matrix) -- compute the inverse
• "inverseSystem(Matrix)" -- see inverseSystem -- Inverse systems with equivariance
• "inverseSystem(ZZ,Matrix)" -- see inverseSystem -- Inverse systems with equivariance
• "isHomogeneous(Matrix)" -- see isHomogeneous -- whether something is homogeneous (graded)
• "isInjective(Matrix)" -- see isInjective -- whether a map is injective
• "isIsomorphic(Matrix,Matrix)" -- see isIsomorphic -- Probabilistic test for isomorphism of modules
• "isIsomorphism(Matrix)" -- see isIsomorphism -- whether a map is an isomorphism
• "isLLL(Matrix)" -- see isLLL -- is a basis an LLL basis?
• "isSurjective(Matrix)" -- see isSurjective -- whether a map is surjective
• "isWellDefined(Matrix)" -- see isWellDefined -- whether a map is well defined
• "jacobianDual(Matrix)" -- see jacobianDual -- Computes the 'jacobian dual', part of a method of finding generators for Rees Algebra ideals
• "jacobianDual(Matrix,Matrix,Matrix)" -- see jacobianDual -- Computes the 'jacobian dual', part of a method of finding generators for Rees Algebra ideals
• kernel(Matrix) -- kernel of a matrix
• kernelLLL(Matrix) (missing documentation)
• 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
• lift(Matrix,type of CC_*,type of CC_*) (missing documentation)
• lift(Matrix,type of RR_*,type of RR_*) (missing documentation)
• "LLL(Matrix)" -- see LLL -- compute an LLL basis
• "LUdecomposition(Matrix)" -- see LUdecomposition -- LU decomposition
• map(Ring,Matrix) -- make a ring map
• map(Ring,Ring,Matrix) -- make a ring map
• markedGB(Matrix,Matrix) -- make a marked Gröbner basis
• Matrix * InfiniteNumber (missing documentation)
• Matrix ** RingElement -- a binary operator, usually used for tensor product or Cartesian product
• "Matrix // RingElement" -- see Matrix // Matrix -- factor a map through another
• /// Matrix \\ Matrix /// -- see Matrix // Matrix -- factor a map through another
• /// Matrix \\ RingElement /// -- see Matrix // Matrix -- factor a map through another
• "RingElement // Matrix" -- see Matrix // Matrix -- factor a map through another
• /// RingElement \\ Matrix /// -- see Matrix // Matrix -- factor a map through another
• Matrix \\ Number (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
• Number \\ Matrix (missing documentation)
• 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
• "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
• resolution(Matrix) -- given a module map represented by a matrix, produce a comparison map between resolutions of its source and target
• "ring(Matrix)" -- see ring -- get the associated ring of an object
• "ringFromFractions(Matrix,RingElement)" -- see ringFromFractions -- find presentation for f.g. ring
• "rsort(Matrix)" -- see rsort -- sort a list or matrix in reverse order
• "simpleDocFrob(ZZ,Matrix)" -- see simpleDocFrob -- a sample documentation node
• smithNormalForm(Matrix) -- smith normal form for a matrix over ZZ or 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,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
• submatrix(Matrix,VisibleList,VisibleList) -- select part of a matrix
• "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
• "symmetricKernel(Matrix)" -- see symmetricKernel -- Compute the Rees ring of the image of a matrix
• target(Matrix) -- find the target module of matrix
• "toDividedPowers(Matrix)" -- see toDividedPowers -- Translates to divided power monomial basis from ordinary monomial basis
• "topCoefficients(Matrix)" -- see topCoefficients -- first variable and its coefficient of a polynomial or matrix
• Tor_ZZ(Ideal,Matrix) (missing documentation)
• Tor_ZZ(Matrix,Ideal) (missing documentation)
• Tor_ZZ(Matrix,Ring) (missing documentation)
• trace(Matrix) -- trace of a matrix
• "vector(Matrix)" -- see vector -- make a vector

For the programmer

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