I'm working on a linear algebra problem that I just cannot wrap my head around.
1) Show that any $n × n$ matrix $A$ of the form $$A = B'B$$ has eigenvalues that are all real and positive. Here, $B$ is any invertible $n × n$ matrix with real or complex entries, and $B'$ is its conjugate transpose
Now I know, any Hermitian matrix $A$ has real eigenvalues, and any matrix $A$ of form $$A = B' B$$ is Hermitian, thus its eigenvalues are real. But I just cannot find out why they should be positive as well.
Any help would be great!