# InnerMatrixLinearAlgebraFunctions(R, Row, Col, M)¶

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

determinant: M -> R
determinant(m) returns the determinant of the matrix m. an error message is returned if the matrix is not square.
generalizedInverse: M -> M
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.