@article{
author = {},
title = {Extended Perron complements of M-matrices},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {26372-26383},
url = {https://www.sciopen.com/article/10.3934/math.20231346},
doi = {10.3934/math.20231346},
abstract = {This paper aims to consider the extended Perron complements for the collection of M-matrices. We first exhibit the connection between the extended Perron complements of M-matrices and nonnegative matrices. Moreover, we present some common inequalities involving extended Perron complements, Schur complements, and principal submatrices of irreducible M-matrices by utilizing the properties of M-matrices. We also discuss the monotonicity of the extended Perron complements and minimum eigenvalue. For the collection of M-matrices, we demonstrate that all (extended) Perron complements are M-matrices. Especially, we deduce that M-matrices and their Perron complements share the same minimum eigenvalue. Finally, a simple example is presented to illustrate our findings.}
}