Use the SVD to show that any square matrix A can be written as A = unitary and P is Hermitian. UP where U is

By SVD, we know that matrix A can be written as

$\begin{array}{l}A=SD{V}^T\\ \text{Where }S\text{ and }V\text{ are orthogonal matrices and}\\ D\text{ is a diagonal matrix whose entries are the singular values of }A.\end{array}$

The singular values of A are the square roots of the eigenvalues of the matrix $A^{H}A$, where $A^H$ is the conjugate transpose of A.