# arrow_back 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].

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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].

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