三次矩阵多项式的谱分解
The Spectral Decomposition of Third Order Matrix Polynomials
DOI: 10.12677/pm.2025.1510247, PDF,    科研立项经费支持
作者: 张 荣, 赵 康*：长沙理工大学数学与统计学院，湖南 长沙
关键词: 矩阵多项式；特征值；谱分解；若尔当对；Matrix Polynomials； Eigenvalue； Spectral Decomposition； Jordan Pair
摘要: 矩阵多项式的谱分解在振动主动控制与被动控制等问题上有广泛的应用。目前，针对二次矩阵多项式的谱分解问题已经有较为完善的研究成果，但尚未见到关于高次矩阵多项式谱分解的研究。本文根据矩阵多项式的若尔当对，给出三次矩阵多项式谱分解的两种不同的证明方法。
Abstract: Spectral decomposition of matrix polynomial has wide applications in active control and passive control. So far, the spectral decomposition problem for quadratic matrix polynomials has been thoroughly studied, while systematic results for the high-order case are still open. Based on the Jordan pair of matrix polynomial, this paper proposes two distinct methods for the spectral decomposition of third-order matrix polynomials.
文章引用：张荣, 赵康. 三次矩阵多项式的谱分解[J]. 理论数学, 2025, 15(10): 40-46. https://doi.org/10.12677/pm.2025.1510247

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