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

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

Ela Rank and Inertia of Submatrices of the Moore–penrose Inverse of a Hermitian Matrix

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.

Ela the Moore - Penrose Inverse of a Free Matrix

A matrix is free, or generic, if its nonzero entries are algebraically independent. Necessary and sufficient combinatorial conditions are presented for a complex free matrix to have a free Moore-Penrose inverse. These conditions extend previously known results for square, nonsingular free matrices. The result used to prove this characterization relates the combinatorial structure of a free matr...

The Moore-Penrose inverse of a free matrix

A matrix is free, or generic, if its nonzero entries are algebraically independent. Necessary and sufficient combinatorial conditions are presented for a complex free matrix to have a free Moore-Penrose inverse. These conditions extend previously known results for square, nonsingular free matrices. The result used to prove this characterization relates the combinatorial structure of a free matr...

the investigation of the relationship between type a and type b personalities and quality of translation

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