# Recent questions tagged hermitian

In a complex vector space (with a hermitian inner product), if a matrix $A$ satisfies $\langle X, A X\rangle=0$ for all vectors $X$, show that $A=0$. [The previous problem shows that this is false in a real vector space].In a complex vector space (with a hermitian inner product), if a matrix $A$ satisfies $\langle X, A X\rangle=0$ for all vectors $X$, show that \ ...