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LAPACK supports computation of both left and right eigenvectors. It would be nice to have a way to get these easily, e.g. from an eigfact object. (We punted on this way back in JuliaLang/julia#160.)
In particular, left eigenvectors are useful in bi-orthogonality relationships for non-Hermitian eigenproblems, in which case you typically want both the left and right eigenvectors. (The left eigenvectors give the inverse of the right-eigenvector matrix.)
evanmiller, matthieugomez and vancleve
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