Finding a matrix from an equation given If $M$ is given in $L'*L^2*L'=M$, can we find $L$? If so how?
We know that $M$ is positive definite matrix. I am working on image processing and solving this challenge can bring several ideas.

Assuming that $M=M'$ and $L=L'$, the you can try the following:


*

*Using Cholesky decomposition, you can obtain that $M = SS'$. $S$ is a lower triangular matrix. It is also invertible.

*At this point, you can say that $L'L^2L' = (L'L)(L'L)' = SS'$. Hence, $L'L = S$


Maybe this can be useful
