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NaturePaper

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I've a simple question (the answer may be so trivial that I really ought to be ashamed for asking!) in elementary matrix theory:

"Does there exists any relation between the number of non-zero eigen values of a matrix with its rank?" The matrix is taken to be a general (square, of course) matrix with complex entries.

[some partial result for full-ranked matrix is known to me, but I want the general relation, if it exists]

What if we restricted to Hermitian (and more specially to Positive semidefinite) matrices?

Thanks & Regards,

Naturepaper