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^*

^*此作品的通讯作者

人工智能学院(人工智能研究院)

Beihang University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

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.

源语言	英语
文章编号	1616
期刊	Mathematics
卷	14
期	10
DOI	https://doi.org/10.3390/math14101616
出版状态	已出版 - 5月 2026

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10.3390/math14101616

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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",

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doi = "10.3390/math14101616",

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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

AN - SCOPUS:105040051046

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

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