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!
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.