I want to have two matrixes of $ A $ and $B$ of a certain size, multiply them together $C = AB$, do some operations on $C$ to make $C_2$ and then decompose the matrix into to matrices of the same size as $A$ and $B$ so that $A_2B_2 = C_2$.
Which decomposition function can I use to achieve this?
EDIT: This is not a duplicate because the thread linked in the comments using LU decomposition says nothing about L and U being the same dimensions as the original matrix