On the Moore-Penrose pseudo-inversion of block symmetric matrices and its application in the graph theory

2022/07/23 by Pavlikova, Sona, Sevcovic, Daniel · 1 citation
#05C50 05B20 05C22 15A09 15A18 15B36 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2207.11563

Abstract

The purpose of this paper is to analyze the Moore-Penrose pseudo-inversion of symmetric real matrices with application in the graph theory. We introduce a novel concept of positively and negatively pseudo-inverse matrices and graphs. We also give sufficient conditions on the elements of a block symmetric matrix yielding an explicit form of its Moore-Penrose pseudo-inversion. Using the explicit form of the pseudo-inverse matrix we can construct pseudo-inverse graphs for a class of graphs which are constructed from the original graph by adding pendent vertices or pendant paths.

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