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This question already has an answer here:

I am as a beginner I want to know is there any relation between eigenvalue and rank of a square matrix Please help.

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marked as duplicate by suomynonA, Dietrich Burde, астон вілла олоф мэллбэрг, Shailesh, Leucippus Jan 31 '17 at 4:22

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    $\begingroup$ Yes, see for example here, or here etc. The question is perhaps too broad. There are many possible answers (too many). $\endgroup$ – Dietrich Burde Jan 28 '17 at 17:09
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The kernel of a matrix is the same as the $0$-eigenspace.

The rank of an $m\times n$ matrix is $m$ minus the dimension of kernel.

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