Properties of Invertible Solutions of the Yang–Baxter-like Matrix Equation for Nonzero Singular Matrix

Xianghui Wen; Di Zhao; Hongyi Li; Chengwei Pan

doi:10.3390/math14101616

Properties of Invertible Solutions of the Yang–Baxter-like Matrix Equation for Nonzero Singular Matrix

Xianghui Wen
, Di Zhao
, Hongyi Li^*
, Chengwei Pan^*

^*Corresponding author for this work

School of Artificial Intelligence(Institute of Artificial Intelligence)

Beihang University

Research output: Contribution to journal › Article › peer-review

Abstract

Assuming the coefficient matrix is a nonzero singular matrix, we demonstrate that the invertible solutions of the Yang–Baxter-like matrix equation must possess at least two elementary divisors. This establishes a necessary condition for an invertible matrix to satisfy the Yang–Baxter-like matrix equation. Building on this finding, we derive several meaningful corollaries. Additionally, we provide some examples to illustrate our results.

Original language	English
Article number	1616
Journal	Mathematics
Volume	14
Issue number	10
DOIs	https://doi.org/10.3390/math14101616
State	Published - May 2026

Keywords

Yang–Baxter-like matrix equation
elementary divisor
group inverse
invertible solutions

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10.3390/math14101616

Cite this

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title = "Properties of Invertible Solutions of the Yang–Baxter-like Matrix Equation for Nonzero Singular Matrix",

abstract = "Assuming the coefficient matrix is a nonzero singular matrix, we demonstrate that the invertible solutions of the Yang–Baxter-like matrix equation must possess at least two elementary divisors. This establishes a necessary condition for an invertible matrix to satisfy the Yang–Baxter-like matrix equation. Building on this finding, we derive several meaningful corollaries. Additionally, we provide some examples to illustrate our results.",

keywords = "Yang–Baxter-like matrix equation, elementary divisor, group inverse, invertible solutions",

author = "Xianghui Wen and Di Zhao and Hongyi Li and Chengwei Pan",

note = "Publisher Copyright: {\textcopyright} 2026 by the authors.",

year = "2026",

month = may,

doi = "10.3390/math14101616",

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volume = "14",

journal = "Mathematics",

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AU - Wen, Xianghui

AU - Zhao, Di

AU - Li, Hongyi

AU - Pan, Chengwei

PY - 2026/5

Y1 - 2026/5

N2 - Assuming the coefficient matrix is a nonzero singular matrix, we demonstrate that the invertible solutions of the Yang–Baxter-like matrix equation must possess at least two elementary divisors. This establishes a necessary condition for an invertible matrix to satisfy the Yang–Baxter-like matrix equation. Building on this finding, we derive several meaningful corollaries. Additionally, we provide some examples to illustrate our results.

AB - Assuming the coefficient matrix is a nonzero singular matrix, we demonstrate that the invertible solutions of the Yang–Baxter-like matrix equation must possess at least two elementary divisors. This establishes a necessary condition for an invertible matrix to satisfy the Yang–Baxter-like matrix equation. Building on this finding, we derive several meaningful corollaries. Additionally, we provide some examples to illustrate our results.

KW - Yang–Baxter-like matrix equation

KW - elementary divisor

KW - group inverse

KW - invertible solutions

UR - https://www.scopus.com/pages/publications/105040051046

U2 - 10.3390/math14101616

DO - 10.3390/math14101616

M3 - 文章

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SN - 2227-7390

VL - 14

JO - Mathematics

JF - Mathematics

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ER -

Properties of Invertible Solutions of the Yang–Baxter-like Matrix Equation for Nonzero Singular Matrix

Abstract

Keywords

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