Expansion formulas for the inertias of Hermitian matrix polynomials and matrix pencils of orthogonal projectors |
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Authors: | Yongge Tian |
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Institution: | China Economics and Management Academy, Central University of Finance and Economics, Beijing 100081, China |
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Abstract: | This paper gives a group of expansion formulas for the inertias of Hermitian matrix polynomials A−A2, I−A2 and A−A3 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. |
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Keywords: | Hermitian matrix Orthogonal projector Partitioned matrix Inertia Rank Equality Inequality Lö wner partial ordering |
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