InnerMatrixLinearAlgebraFunctions(R, Row, Col, M)

matfuns.spad line 1 [edit on github]

• R: DivisionRing

• Row: FiniteLinearAggregate R

• Col: FiniteLinearAggregate R

• M: MatrixCategory(R, Row, Col)

InnerMatrixLinearAlgebraFunctions is an internal package which provides standard linear algebra functions on domains in MatrixCategory

determinant: M -> R if R has Field

determinant(m) returns the determinant of the matrix m. an error message is returned if the matrix is not square.

generalizedInverse: M -> M if R has Field

generalizedInverse(m) returns the generalized (Moore–Penrose) inverse of the matrix m, i.e. the matrix h such that m*h*m=h, h*m*h=m, m*h and h*m are both symmetric matrices.

inverse: M -> Union(M, failed)

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

nullity: M -> NonNegativeInteger

nullity(m) returns the mullity of the matrix m. This is the dimension of the null space of the matrix m.

nullSpace: M -> List Col if Col has shallowlyMutable

nullSpace(m) returns a basis for the null space of the matrix m.

rank: M -> NonNegativeInteger

rank(m) returns the rank of the matrix m.

row_operation_base: (M, Integer, Integer, Integer, Integer, R) -> Void

row_operation_base should be local, but conditional

row_operation_modular: (M, Integer, Integer, Integer, Integer, R, Integer) -> Void

row_operation_modular should be local, but conditional

rowEchelon: M -> M

rowEchelon(m) returns the row echelon form of the matrix m.