AbstractAlgebra provides matrix spaces (mxn matrices) and matrix algebras (nxn matrices) over a ring. Whilst both types of matrix provide matrix multiplication for matrices whose dimensions are compatible for multiplication, only the latter kind of matrices form rings in the system.

Matrix spaces provide a large number of linear algebra operations, including linear solving, elementary row operations, various canonical forms. The system also provides characteristic and minimal polynomial computations, LU decomposition, determinant, matrix inverse, kernel computations.

There is also code for computation of the Hermite and Smith normal forms over Euclidean domains and Popov form for matrices over polynomial rings over a field.

Most of this generic functionality is provided for arbitrary matrix types that satisfy the AbstractAlgebra matrix interface.