Rank and inertia of submatrices of the Moore-Penrose inverse of a Hermitian matrix

Yongge Tian

doi:10.13001/1081-3810.1370

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Published: Jan 1, 2010

DOI: https://doi.org/10.13001/1081-3810.1370

Keywords:

Hermitian Matrix, Partitioned Matrix, Moore-Penrose inverse, Rank, Inertia

Yongge Tian

Abstract

Closed-form formulas are derived for the rank and inertia of submatrices of the Moore–Penrose inverse of a Hermitian matrix. A variety of consequences on the nonsingularity, nullity and deﬁniteness of the submatrices are also presented.

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Vol. 20 (2010)

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