Must the left eigenvectors and right eigenvectors of a matrix be the same? Prove or give counter example.

I want to say no, but am not sure if I am even correct let alone proving. Can someone help me out? Thanks!

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- Nov 27th 2011, 11:58 AMpage929Left and Right Eigenvectors
Must the left eigenvectors and right eigenvectors of a matrix be the same? Prove or give counter example.

I want to say no, but am not sure if I am even correct let alone proving. Can someone help me out? Thanks! - Nov 27th 2011, 02:20 PMHallsofIvyRe: Left and Right Eigenvectors
If by "left eigenvalue" you mean a value of [itex]\lambda[/itex] such that

and by "right eigenvalue", you mean a value of [itex]\lambda[/itex] such that

Then the "right eigenvalues" of A are the "left eigenvalues" of the**transpose**of A.