# Thread: Cholesky decomposition of kronecker product

1. ## Cholesky decomposition of kronecker product

Hi,

Is there any proof that $cholesky(A\otimes B)=cholesky(A)\otimes cholesky(B)$ for $A$ and $B$ symmetric?
It seems correct for $2\times 2$-matrices, but is it in general?

2. ## Re: Cholesky decomposition of kronecker product

Originally Posted by SimonDR
Hi,

Is there any proof that $cholesky(A\otimes B)=cholesky(A)\otimes cholesky(B)$ for $A$ and $B$ symmetric?
It seems correct for $2\times 2$-matrices, but is it in general?
It looks like yes.

http://www.math.uwaterloo.ca/~hwolko...schaecke04.pdf

might be of some help