A generalization of Weyl's inequalities with implications

This paper suggests a generalization of additive Weyl's inequalities to the case of two square matrices of different orders. As a consequence of generalized Weyl's inequalities, a theorem describing the location of eigenvalues of a Hermitian matrix in terms of the eigenvalues of an arbitrary Hermitian matrix of smaller order is derived. It is demonstrated that the latter theorem provides a generalization of Kahan's theorem on clustered eigenvalues. Also it is shown that the theorem on extended interlacing intervals established in [3] is another consequence of the generalized additive Weyl inequalities suggested.