# Why are the eigenvalues of $X'X$ equal to that of $XX'$ when $X$ is a design matrix?

by qualiaMachine   Last Updated September 11, 2019 16:19 PM

The title says it all. If $$X$$ is a design matrix (columns containing variables, rows containing observations), I have observed that eigs($$X'X$$)=eigs($$XX'$$). I actually found this by accident when I was trying to compute eigenvalues of a covariance matrix in Matlab. Why is this the case? Can someone provide me some intuition, proofs, and/or reading materials?

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