If M is the tuple module R^((m)) and N is the tuple module R^((n)), create the module Hom_(R)(M, N) as the (R, R)-bimodule R^((m x n)), represented as the set of all m x n matrices over R. The module is created with the standard basis, {E_(ij) | i = 1 ..., m, j = 1 ..., n}, where E_(ij) is the matrix having a 1 in the (i, j)-th position and zeros elsewhere.

Given a ring R and positive integers m and n, construct H = Hom(M, N), where M = R^((m)) and N = R^((n)), as the free (R, R)-bimodule R^((m x n)), consisting of all m x n matrices over R. The module is created with the standard basis, {E_(ij) | i = 1 ..., m, j = 1 ..., m}. Note that the modules M and N are created by this function and may be accessed as Domain(H) and Codomain(H), respectively.

If M is the free R-module R^((m)), create the matrix algebra Mat_m(R). The algebra is created with the standard basis, {E_(ij) | i = 1 ..., m, j = 1 ..., m}, where E_(ij) is the matrix having a 1 in the (i, j)-th position and zeros elsewhere.

> F2 := GaloisField(2);
> V  := VectorSpace(F2, 3);
> W  := VectorSpace(F2, 4);
> M  := Hom(V, W);
> print M;
Full KMatrixSpace of 3 by 4 matrices over GF(2)

> Q  := RationalField();
> R4 := RModule(Q, 4);
> M  := EndomorphismAlgebra(R4);
> print M;
Full Matrix Algebra of degree 4 over Rational Field