Abstract
<abstract><p>This paper aims to consider the extended Perron complements for the collection of <italic>M</italic>-matrices. We first exhibit the connection between the extended Perron complements of <italic>M</italic>-matrices and nonnegative matrices. Moreover, we present some common inequalities involving extended Perron complements, Schur complements, and principal submatrices of irreducible <italic>M</italic>-matrices by utilizing the properties of <italic>M</italic>-matrices. We also discuss the monotonicity of the extended Perron complements and minimum eigenvalue. For the collection of <italic>M</italic>-matrices, we demonstrate that all (extended) Perron complements are <italic>M</italic>-matrices. Especially, we deduce that <italic>M</italic>-matrices and their Perron complements share the same minimum eigenvalue. Finally, a simple example is presented to illustrate our findings.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
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