类杨-巴克斯特矩阵方程AXA = XAX的所有解，其中A满足A4 = A

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-10 DOI:10.1016/j.jmaa.2025.129785

Duanmei Zhou , Jie Liao , Yudan Gan , Huilin Xu , Rong Zhang

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引用次数: 0

摘要

对于满足A4=A的矩阵A，构造了类yang - baxter矩阵方程AXA=XAX的若干显式解，从而推广了这一领域的前人成果。通过分析A的最小多项式，我们将问题分为11种不同的情况。我们的方法利用A的约旦分解来简化原始方程，将其简化为包含较小块的块对角矩阵的矩阵方程系统。然后系统地求解这些化简方程，得到通解。最后，通过三个数值算例验证了理论结果的适用性和有效性。

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All solutions of the Yang-Baxter-like matrix equation AXA = XAX with A satisfying A4 = A

In this paper, we construct some explicit solutions to the Yang-Baxter-like matrix equation

A X A = X A X

for matrices A satisfying

A^{4} = A

, thereby extending previous results in this field. By analyzing the minimal polynomial of A, we classify the problem into 11 distinct cases. Our approach leverages the Jordan decomposition of A to simplify the original equation, reducing it to a system of matrix equations involving block-diagonal matrices with smaller blocks. We then systematically solve these reduced equations to obtain the general solution. Finally, we present three numerical examples to demonstrate the applicability and effectiveness of our theoretical results.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.

类杨-巴克斯特矩阵方程AXA = XAX的所有解，其中A满足A4 = A

摘要

类杨-巴克斯特矩阵方程AXA = XAX的所有解，其中A满足A4 = A