Is the matrix $A^*A$ and $AA^*$ hermitian?
As the title says. Is the matrices $A^*A$ and $AA^*$ hermitian (symmetric if $A$ is real)?
Solution 1:
Check the definition of hermitian. This is not too hard, you just have to use that $(AB)^*=B^*A^*$. You don't need that $A$ is invertible in this proof, the statement is even true for $A$ not a square.