I am interested in results on the eigenvalues of submatrices.

Given a symmetric and positive-semidefinite matrix $M$, denote the submatrix obtained by deleting the ith column and jth row as $[M]_{ji}$.

How does the spectra $\lambda([M]_{ji})$ relate to the spectra $\lambda(M)$?

I know when looking at principal submatrices (ie, $i=j$), we get an interlacing property. However, I can't seem to find such results for other submatrices.