Expressions and characterizations for the Moore-Penrose inverse
Patricia Mariela Morillas
TL;DR
This paper derives new expressions and characterizations for the Moore-Penrose inverse of operators, including sums, matrices, circulant matrices, and graph distance matrices, aiding its computation.
Contribution
It provides novel formulas and characterizations for the Moore-Penrose inverse, especially for sums of operators and specific matrix classes.
Findings
Sum of Moore-Penrose inverses equals inverse of sum under certain conditions
Formulations for finite matrices and circulant matrices
Analysis of Moore-Penrose inverse of graph distance matrices
Abstract
Under certain conditions, we prove that the Moore-Penrose inverse of a sum of operators is the sum of the Moore-Penrose inverses. From this, we derive expressions and characterizations for the Moore-Penrose inverse of an operator that are useful for its computation. We give formulations of them for finite matrices and study the Moore-Penrose inverse of circulant matrices and of distance matrices of certain graphs.
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Taxonomy
TopicsMatrix Theory and Algorithms · graph theory and CDMA systems · Advanced Topics in Algebra