Can B Be Determined from Given A and C in Kronecker Product?

[umut_caglar]

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 $A \otimes B = C$

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.

 

[fresh_42]

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.