Finding the common eigenvectors of two matrices

Question

I want to find the common eigenvectors of two symmetric matrices with the same dimension in R Assuming two matrices L1 and L2 I am looking for vector X such that L1*X = (landa)L2*X where landa is the eigen value

Answer 1

The term you are looking for is Generalized Eigenvalue Problem. This is a well researched linear algebra problem.

In terms of implementation, I suggest looking at a special Netlib section, where I think your matrices will satisfy Generalized Symmetric Definite Eigenproblems solver requirements.

Intel MKL provides the functionality directly available from C, Fortran, and, as far as I know, Python.