## Minimise difference between two matrices

Hello,

I have been told that I need to minimise the error between two matrices, like so.

$\displaystyle {A_1}x = {A_2}s$

Where A_1 and A_2 are convolution folding matrices. x represents the desired filter and s the actual filter. I need to minimise the error between x and s. So using Cholesky, I would do this

$\displaystyle x = {({A^T}_1{A_1})^{ - 1}}{A_2}s$

but the answer in my book is:

$\displaystyle x = {({A^T}_1{A_1})^{ - 1}}{A_1}{A_2}s$

Can someone explain how that answer was derived?

Thanks.