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1. Expansion formulas for the inertias of Hermitian matrix polynomials and matrix pencils of orthogonal projectors

Author

Tian, Yongge

Subjects
*HERMITIAN operators, *MATHEMATICAL formulas, *POLYNOMIALS, *MATRIX pencils, *MATHEMATICAL inequalities, *ORTHOGRAPHIC projection
Abstract

Abstract: This paper gives a group of expansion formulas for the inertias of Hermitian matrix polynomials , and through some congruence transformations for block matrices, where A is a Hermitian matrix. Then, the paper derives various expansion formulas for the ranks and inertias of some matrix pencils generated from two or three orthogonal projectors and Hermitian unitary matrices. As applications, the paper establishes necessary and sufficient conditions for many matrix equalities to hold, as well as many inequalities in the Löwner partial ordering to hold. [Copyright &y& Elsevier]

Published
2011
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