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.
Citation: Qin Zhong, Ling Li. Notes on the generalized Perron complements involving inverse $ {{N}_{0}} $-matrices[J]. AIMS Mathematics, 2024, 9(8): 22130-22145. doi: 10.3934/math.20241076
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.
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Qin Zhong, Ling Li. Notes on the generalized Perron complements involving inverse $ {{N}_{0}} $-matrices[J]. AIMS Mathematics, 2024, 9(8): 22130-22145. doi: 10.3934/math.20241076
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