# Tensor Product of Two Matrices coming from Algebra Representations

Is there a command in sage to compute the tensor product of two Matrices coming from Algebra representations? In groups, x(v tensor w) = xv tensor xw, and the sage command Matrix1.tensor_product(Matrix2) appears to give the matrix corresponding to this. But in an algebra x(v tensor w) = xv tensor w + v tensor xw. How can I compute the corresponding matrix here?

edit retag close merge delete

What you need is perhaps "tensor sum", "Kronecker sum".

( 2013-11-13 05:51:06 +0200 )edit

Sort by ยป oldest newest most voted

Hi,

If M1 is your first matrix (of dimension n1) and M2 is your second matrix (of dimension n2), then the answer should be:

M1.tensor_product(identity_matrix(n2)) +
identity_matrix(n1).tensor_product(M2)


Vincent

more

M1 "tensor_sum" M2 = eye(n2) "tensor_product" M1 + eye(n1) "tensor_product" M2 .. the tensor product operation is not commutative, I guess. Hence, identity_matrix(n2).tensor_product(M1) + M2.tensor_product(identity_matrix(n1)) , or?

( 2013-11-13 05:54:20 +0200 )edit

but this command is too long.. we have to write a my_function or the function "tensor_sum" is already implemented in some packages, such as maxima, Scipy ....

( 2013-11-13 05:57:16 +0200 )edit