The following function computes eigen values and eigen vectors for square matrix. But I don’t understand what is W?

[V,LAMBDA,W] = eig(A) where A is the square matrix.

V is right eigen vector( ) of square matrix A.

And I think W is also an left eigen vector( ) of square matrix A.

I get in octave A × V = V × LAMBDA, but I didn’t get A × W = W × LAMBDA or W × A = W × LAMBDA. where A × V = matrix multiplication

How is that?