On free matrices

Thomas Britz

On free matrices

Thomas Britz

Research output: Book/Report › Report › Research

Abstract

Bipartite graphs and digraphs are used to describe algebraic operations on a free matrix, including Moore-Penrose inversion, finding Schur complements, and normalized LU factorization. A description of the structural properties of a free matrix and its Moore-Penrose inverse is proved, and necessary and sufficient conditions are given for the Moore-Penrose inverse of a free matrix to be free. Several of these results are generalized with respect to a family of matrices that contains both the free matrices and the nearly reducible matrices.

Original language	English

Place of Publication	København
Publisher	Department of Mathematics, Technical University of Denmark
Edition	1
Publication status	Published - 2004

Series	MAT-Report
Number	2004-15

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On free matrices

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