I've been reading everywhere, including wikipedia, and I can't seem to find a prove to the fact that the covariance matrix of a complex random vector is Hermitian positive definitive. Why is it definitive and not just simple semi-definitive like any other covariance matrix?(adsbygoogle = window.adsbygoogle || []).push({});

Wikipedia just states this and never provides with a prove. Some people might say that it follows from the definition and that a prove is trivial, but I just can't seem to find why. Even if the prove is trivial (and it's eluding me) can somebody please demonstrate why?

Also, if this is true, does it also apply for crosscovariance matrix? (between two different complex random vectors)

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# Covariance matrix

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