# Generalized eigenvalue problem using ARPACK

Is it possible to solve the eigenvalue problem:

$$Ax = \lambda Mx$$

using ARPACK when $A$ and $M$ are both non-symmetric complex matrices? According to this documentation, the function znaupd only works when $M$ is symmetric positive definite. I have verified that the results are only correct when $M$ meets this requirement. I have heard that Matlab's eigs function is loosely based on ARPACK and it is able to handle non-symmetric $M$ matrices. Do they just convert it to a standard eigenvalue problem?

If this is not possible using ARPACK, what are some alternatives?

After reading the documentation closer, it recommends converting the problem to a standard eigenvalue problem when $A$ and $M$ are non-Hermitian positive semi-definite. Section 3.2.2 from the ARPACK documentation: