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

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`.