Core-monotonicity characterizations for nonnegative matrices

Journal of Lanzhou University of Technology ›› 2025, Vol. 51 ›› Issue (3): 167-172.

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Core-monotonicity characterizations for nonnegative matrices

LIN Lin¹, ZHONG Jin²

1. Department of Basic Courses, Nanchang Jiaotong Institute, Nanchang 330100, China;
2. Faculty of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China

Received:2023-05-10 Online:2025-06-28 Published:2025-06-30

Abstract

Abstract: Characterizations for the core-monotonicity of nonnegative matrices are studied. A sufficient and necessary condition for core-monotonicity of nonnegative matrices is presented by nonnegative full-rank decomposition, and the representation of the core inverse is also given when it is nonnegative. It is shown by some numerical examples that the nonnegativity of the core inverse and the Moore-Penrose is not equivalent to the group inverse of nonnegative matrices. Furthermore, a sufficient and necessary condition for the core-monotonicity of nonnegative matrices is given by using the Moore-Penrose inverse and group inverse. Additionally, a sufficient and necessary condition for the core-monotonicity of real matrices is presented, which extends the results of Collatz.

Key words: nonnegative matrix, core inverse, core-monotonicity, dual core-monotonicity

CLC Number:

O151.21

LIN Lin, ZHONG Jin. Core-monotonicity characterizations for nonnegative matrices[J]. Journal of Lanzhou University of Technology, 2025, 51(3): 167-172.

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Core-monotonicity characterizations for nonnegative matrices

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