Tensor Product of Two Matrices coming from Algebra Representations

ChrisBerg
1 ●1 ●1 ●1

vdelecroix
7640 ●20 ●85 ●168 http://www.labri.fr/pe...

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?

Comments

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

gundamlh ( 11 years ago )

add a comment

answered 12 years ago

vdelecroix
7640 ●20 ●85 ●168 http://www.labri.fr/pe...

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

link

Comments

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?

gundamlh ( 11 years ago )

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 ....

gundamlh ( 11 years ago )

add a comment

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Tensor Product of Two Matrices coming from Algebra Representations

Comments

1 Answer

Comments

Your Answer

Question Tools

Stats

Related questions

Tensor Product of Two Matrices coming from Algebra Representations savecancel

Comments

1 Answer

Comments

Your Answer

Question Tools

Stats

Related questions

Tensor Product of Two Matrices coming from Algebra Representations