Extensions of Wielandt's Min-max Principles for Positive Semi-Definite Pencils

There are numerous min-max principles about the eigenvalues of a Hermitian matrix. The most general ones are Wielandt’s min-max principles which include the Courant-Fisher min-max principles and the trace minimization principles as special cases. In this paper, various extensions of Wielandt’s principles are obtained for a positive semi-definite pencil A − λB by which we mean that A and B are Hermitian and there is a real number λ0 such that A− λ0B is positive semi-definite.