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manipulating matrices

Some simple information about matrices:

  • degree Matrix -- the degree
  • degrees Matrix -- degrees of generators
  • entries Matrix -- list the entries of a matrix
  • isHomogeneous Matrix -- test for homogeneity
  • ring Matrix -- get the associated ring
  • source Matrix -- source of a map
  • target Matrix -- target of a map
  • trace Matrix -- trace of a matrix
  • Matrix _ (...) -- get an entry
  • Matrix == ZZ -- equality
  • Some common algebraic operations on matrices:

  • Matrix + Matrix -- a binary operator
  • - Matrix -- a unary or binary operator, usually used for negation or subtraction
  • Matrix - Matrix -- a unary or binary operator, usually used for negation or subtraction
  • Matrix * Matrix -- matrix multiplication
  • Matrix ^ ZZ -- a binary operator, usually used for exponents
  • Matrix == Matrix -- equality
  • Matrix ** Matrix -- tensor product of matrices
  • Matrix // Matrix -- factor a map through another
  • Matrix % Matrix -- find the normal form modulo the image of a map
  • Matrix ++ Matrix -- direct sum of maps
  • Matrix | Matrix -- join matrices horizontally
  • Matrix || Matrix -- join matrices vertically
  • Matrix ^ {...} -- select some rows of a matrix
  • Matrix _ {...} -- get some columns from a matrix
  • sortColumns Matrix -- sort the columns of a matrix
  • submatrix(Matrix,{...},{...}) -- select part of a matrix
  • substitute(Matrix,{...}) -- substitute values for variables
  • substitute(Matrix,Matrix) -- substitute values for variables
  • transpose Matrix -- transpose
  • Some computations on matrices:

  • exteriorPower(ZZ,Matrix) -- exterior power
  • isInjective Matrix -- whether a map is injective
  • isSurjective Matrix -- whether a map is surjective
  • isIsomorphism Matrix -- whether a map is an isomorphism
  • pfaffians(ZZ,Matrix) -- ideal generated by Pfaffians
  • rank Matrix -- compute the rank
  • symmetricPower(ZZ,Matrix) -- symmetric power

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