Notes on the generalized Perron complements involving inverse $ {{N}_{0}} $-matrices

Abstract

In the context of inverse $ {{N}_{0}} $-matrices, this study focuses on the closure of generalized Perron complements by utilizing the characteristics of $ M $-matrices, nonnegative matrices, and inverse $ {{N}_{0}} $-matrices. In particular, we illustrate that the inverse $ {{N}_{0}} $-matrix and its Perron complement matrix possess the same spectral radius. Furthermore, we present certain general inequalities concerning generalized Perron complements, Perron complements, and submatrices of inverse $ {{N}_{0}} $-matrices. Finally, we provide specific examples to verify our findings.

Keywords

• $ {{n}_{0}} $-matrix
• inverse $ {{n}_{0}} $-matrix
• generalized perron complement
• spectral radius
• schur complement