Please consider clarifying the documentation of

> help eig

where the option to compute eigenvalues, right eigenvectors and left eigenvectors is described as follows.

 -- [V, LAMBDA, W] = eig (A)
 Compute the eigenvalues (LAMBDA) and optionally the right
 eigenvectors (V) and the left eigenvectors (W) of a matrix or pair
 of matrices.

The left eigenvectors are mathematically row vectors. However, the underlying LAPACK routine trevc3 computes the left eigenvectors as columns, probably for performance reasons. The fact that the left eigenvectors are stored in (conjugate) transpose form should be explicitly documented, for example by something like:

The eigenvectors are stored columnwise such that the right eigenvectors satisfy A*V=LAMBDA*V and the left eigenvectors satisfy W'*A=LAMBDA*W'.

For reference, Matlab documents:

[V,D,W] = eig(A) also returns full matrix W whose columns are the corresponding left eigenvectors, so that W'*A = D*W'.