Skew compressions of positive definite operators and matrices

The paper is devoted to results connecting the eigenvalues and singular values of operators composed by $P^\ast G P$ with those composed in the same way by $QG^{−1}Q^\ast$. Here $P +Q = I$ are skew complementary projections on a finite-dimensional Hilbert space and $G$ is a positive definite linear operator on this space. Also discussed are graph theoretic interpretations of one of the results.