Can you show that the range space and the null space of a Hermitian matrix are mutually orthogonal. I was reading a conference paper and they used it too easily I suppose. Can you please prove.
2026-03-26 12:40:17.1774528817
Hermitian Matrix
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Let $H$ be a Hermitian matrix. Let $u$ be a vector such that $Hu=0$, and $v$ be any vector.
$$\left<u,Hv\right>=\left<H^*u,v\right>=\left<Hu,v\right>=\left<0,v\right>=0$$