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Tensor Product of Two Matrices coming from Algebra Representations

asked 2011-05-03 11:06:56 +0200

ChrisBerg gravatar image

updated 2012-08-04 00:18:20 +0200

vdelecroix gravatar image

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?

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

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

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answered 2012-08-03 23:50:26 +0200

vdelecroix gravatar image

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

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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 gravatar imagegundamlh ( 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 ....

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

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Asked: 2011-05-03 11:06:56 +0200

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Last updated: Aug 03 '12