I am as a beginner I want to know is there any relation between eigenvalue and rank of a square matrix Please help.
Eigen value and rank of a matrix
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eigenvalues-eigenvectors
matrix-rank
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1Yes, see for example [here](http://math.stackexchange.com/questions/1349907/what-is-the-relation-between-rank-of-a-matrix-its-eigenvalues-and-eigenvectors), or [here](http://math.stackexchange.com/questions/159232/relationship-rank-of-a-matrix-leftrightarrow-of-eigenvalues?rq=1) etc. The question is perhaps too broad. There are many possible answers (too many). – 2017-01-28
1 Answers
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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.