The matrix algebra M_n(S) may also be viewed as the module Hom(S^((n)), S^((n))). At present this will not happen automatically so that in order to treat elements of M_n(S) as homomorphisms, it is necessary to explicitly coerce the matrix into Hom(S^((n)), S^((n))). However, two fundamental homomorphism-type operators are provided for elements of M_n(S).

Image(a) : AlgMatElt -> ModTup

RowSpace(a) : AlgMatElt -> ModTup

Given an element of M_n(S), return the image of the module S^((n)) under the homomorphism represented by the matrix a (as an element of S^((n))).

NullSpace(a) : AlgMatElt -> ModTup

Given an element of M_n(S), return the kernel of the homomorphism represented by the matrix a (as an element of S^((n))).

Given an element of M_n(S), return the row nullspace of the homomorphism represented by the matrix a (as an element of S^((n))). This is equal to the kernel of the transpose of a.