Given two matrix algebras R and T, where R and T have the same coefficient ring S, return the direct sum D of R and T (with the action given by the direct sum of the action of R and the action of T).
Given two unital matrix algebras A and B, where A and B have the same coefficient ring S, construct the tensor product of A and B.
> Q := RationalField();
> A := MatrixAlgebra< Q, 3 | [ 1/3,0,0, 3/2,3,0, -1/2,4,3],
> [ 3,0,0, 1/2,-5,0, 8,-1/2,4] >;
> AplusA := DirectSum(A, A);
> AplusA: Maximal;
Matrix Algebra of degree 6 with 4 generators over
Rational Field
Generators:
[ 1/3 0 0 0 0 0]
[ 3/2 3 0 0 0 0]
[-1/2 4 3 0 0 0]
[ 0 0 0 0 0 0]
[ 0 0 0 0 0 0]
[ 0 0 0 0 0 0]
[ 3 0 0 0 0 0]
[ 1/2 -5 0 0 0 0]
[ 8 -1/2 4 0 0 0]
[ 0 0 0 0 0 0]
[ 0 0 0 0 0 0]
[ 0 0 0 0 0 0]
[ 0 0 0 0 0 0]
[ 0 0 0 0 0 0]
[ 0 0 0 0 0 0]
[ 0 0 0 1/3 0 0]
[ 0 0 0 3/2 3 0]
[ 0 0 0 -1/2 4 3]
[ 0 0 0 0 0 0]
[ 0 0 0 0 0 0]
[ 0 0 0 0 0 0]
[ 0 0 0 3 0 0]
[ 0 0 0 1/2 -5 0]
[ 0 0 0 8 -1/2 4]
> AtimesA := TensorProduct(A, A);
> AtimesA: Maximal;
Matrix Algebra of degree 9 with 4 generators over
Rational Field
Generators:
[ 1/3 0 0 0 0 0 0 0 0]
[ 0 1/3 0 0 0 0 0 0 0]
[ 0 0 1/3 0 0 0 0 0 0]
[ 3/2 0 0 3 0 0 0 0 0]
[ 0 3/2 0 0 3 0 0 0 0]
[ 0 0 3/2 0 0 3 0 0 0]
[-1/2 0 0 4 0 0 3 0 0]
[ 0 -1/2 0 0 4 0 0 3 0]
[ 0 0 -1/2 0 0 4 0 0 3]
[ 3 0 0 0 0 0 0 0 0]
[ 0 3 0 0 0 0 0 0 0]
[ 0 0 3 0 0 0 0 0 0]
[ 1/2 0 0 -5 0 0 0 0 0]
[ 0 1/2 0 0 -5 0 0 0 0]
[ 0 0 1/2 0 0 -5 0 0 0]
[ 8 0 0 -1/2 0 0 4 0 0]
[ 0 8 0 0 -1/2 0 0 4 0]
[ 0 0 8 0 0 -1/2 0 0 4]
[ 1/3 0 0 0 0 0 0 0 0]
[ 3/2 3 0 0 0 0 0 0 0]
[-1/2 4 3 0 0 0 0 0 0]
[ 0 0 0 1/3 0 0 0 0 0]
[ 0 0 0 3/2 3 0 0 0 0]
[ 0 0 0 -1/2 4 3 0 0 0]
[ 0 0 0 0 0 0 1/3 0 0]
[ 0 0 0 0 0 0 3/2 3 0]
[ 0 0 0 0 0 0 -1/2 4 3]
[ 3 0 0 0 0 0 0 0 0]
[ 1/2 -5 0 0 0 0 0 0 0]
[ 8 -1/2 4 0 0 0 0 0 0]
[ 0 0 0 3 0 0 0 0 0]
[ 0 0 0 1/2 -5 0 0 0 0]
[ 0 0 0 8 -1/2 4 0 0 0]
[ 0 0 0 0 0 0 3 0 0]
[ 0 0 0 0 0 0 1/2 -5 0]
[ 0 0 0 0 0 0 8 -1/2 4]
Given an element a of the matrix algebra Q and an element b of the matrix algebra R, form the direct sum of matrices a and b. The square is returned as an element of the matrix algebra T, which must be the direct sum of the parent of a and the parent of b.
Given an element a of the matrix algebra M_n(S), form the exterior square of a as an element of M_m(S), where m = n(n - 1)/2.
Given an element a of the matrix algebra M_n(S), form the symmetric square of a as an element of M_m(S), where m = n(n + 1)/2.
Given an element a belonging to a subalgebra of M_(n_1)(S) and an element b belonging to a subalgebra of M_(n_2)(S), construct the tensor product of a and b as an element of the matrix algebra M_n(S), where n = n_1 * n_2.[Next] [Prev] [Right] [Left] [Up] [Index] [Root]