Let $h$ be a positive definite hermitian form on $E$ and $A,B: E\rightarrow E$ be two hermitian endomorphisms which commute, $AB = BA$. Prove that there exists a orthogonal basis for $E$ consisting of common eigenvectors for $A$ and $B$.
Serge Lange,"Algebra" Chapter 15,Question 4
Can you please give any hint?