# Product of hermitian and unitary matrix is a square matrix?

I am unable to think of a way to prove this result: Show that every square matrix is a product of a hermitian matrix and an unitary matrix.

I want to prove it using the spectral theorem.

Thanks for the help.

This is usually done via the "polar decomposition" of a matrix; more information on that is given here. This answer details what that looks like for real matrices; a similar proof applies in the complex case, where the $T$'s are replaced by $*$'s.
• The spectral theorem provides a convenient way to show that $A^*A$ has a unique positive definite square root. – Omnomnomnom Sep 1 '17 at 14:17