As discussed in #1175, right now mathjs can only find eigenvalues of real symmetric matrices. It should also be able to find the eigenvalues and eigenvectors for general complex matrices. I'm consulting Numerical recipes in Fortran 77 when working on this issue.

The steps that need to be implemented in order to solve the eigenproblem are the following:

• Balancing (for numeric stability; perform a similarity transform to make the norms of corresponding row-column pairs close to each other)
• Reduce to Hessenberg form (upper triangular plus one subdiagonal; using Gaussian elimination)
• Perform the QR algorithm for Hessenberg matrices