MatrixCategory

Exports

• CopyableType
  LinearArithmeticType R
  $*$:	(%,V) $\to$ V	multiplication by a vector
  $[]$:	Tuple V $\to$ %	create a matrix
  	Generator V $\to$ %
  apply:	(%,I,I) $\to$ R	extract an entry
  apply:	(%,I,I,I,I) $\to$ %	extract a submatrix
  colCombine!:	(%,R,I,R,I) $\to$ %	In-place linear combination of columns
  	(%,R,I,R,I,I,I) $\to$ %
  	(%,(R,R)$\to$ R,I,I) $\to$ %
  	(%,(R,R)$\to$ R,I,I,I,I) $\to$ %
  colSwap!:	(%,I,I) $\to$ %	Swap columns in-place
  	(%,I,I,I,I) $\to$ %
  column:	(%,I) $\to$ V	extraction of a column
  columns:	% $\to$ Generator V	iteration over the columns
  companion:	V $\to$ %	creates a companion matrix
  	(V, R) $\to$ %
  diagonal:	V $\to$ %	creates a diagonal matrix
  diagonal?:	% $\to$ Boolean	test for a diagonal matrix
  dimensions:	% $\to$ (I,I)	get row and column dimensions
  map:	(R $\to$ R) $\to$ V $\to$ %	lift a mapping
  map:	(R $\to$ R) $\to$ % $\to$ %	lift a mapping
  map!:	(R $\to$ R) $\to$ % $\to$ %	lift a mapping
  numberOfColumns:	% $\to$ I	number of columns of the matrix
  numberOfRows:	% $\to$ I	number of rows of the matrix
  one:	I $\to$ %	identity matrix
  one?:	% $\to$ Boolean	test for an identity matrix
  row:	(%,I) $\to$ V	extraction of a row
  rowCombine!:	(%,R,I,R,I) $\to$ %	In-place linear combination of rows
  	(%,R,I,R,I,I,I) $\to$ %
  	(%,(R,R)$\to$ R,I,I) $\to$ %
  	(%,(R,R)$\to$ R,I,I,I,I) $\to$ %
  rowSwap!:	(%,I,I) $\to$ %	Swap rows in-place
  	(%,I,I,I,I) $\to$ %
  rows:	% $\to$ Generator V	iteration over the rows
  set!:	(%,I,I,R) $\to$ R	set an entry in the matrix
  setMatrix!:	(%,I,I,%) $\to$ %	modify a submatrix of a matrix
  square?:	% $\to$ Boolean	test for a square matrix
  tensor:	(%, %) $\to$ %	tensor product
  transpose:	V $\to$ %	transpose a vector
  transpose:	% $\to$ %	transpose a matrix
  transpose!:	% $\to$ %	transpose a matrix in-place
  zero:	(I,I) $\to$ %	create a zero matrix
  zero!:	% $\to$ ()	make all the entries zero
  zero?:	% $\to$ Boolean	test if all entries are zero

• if R has Ring then
  

• random:	() $\to$ %	create a random matrix
  	(I,I) $\to$ %

• if R has DifferentialRing then
  

• wronskian:

  V $\to$ %

  Wronskian matrix

• where

• I	==	MachineInteger
  V	==	Vector R

• if $R$ has SerializableType then
  

• SerializableType