Kronecker product decomposition

  • #1
hi everybody

Today I have a question about Kronecker products, If you have a direct answer it is perfect but if not, any kind of paper reference might work as well.

now say I have to matrices A and B in general there is nothing special about them. They are not hermitian or triangular or what ever special.

then I calculate the Kronecker product between them


[itex]A \otimes B = C[/itex]

then assume that A and C is given to us and we want to figure out what B is. I know that B is not unique but is there anything that we can say about B? Do you know any algorithm that can give some predictions or guesses for B.

I know one stuff that can approximately decompose C into a A', B' pair. But in this algorithm you do not have any control on A or B.

http://www.mit.edu/~wingated/scripts/krondecomp.m

any idea is welcome, thank you.
 

Answers and Replies

  • #2
13,560
10,662
Given ##A## and ##C## makes ##B## unique. The elements of ##C## are pairs ##c_{ijkl}=a_{ij}b_{kl}##. Tensor products are not unique in the sense that ##\lambda A\oplus B = A \oplus \lambda B##. But as you nailed ##A##, there are no scalars ##\lambda \neq 1## which can be swapped. Also, as you have only a dyade, sums don't have any effect either, as there are simply none.
 

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