| 摘要: |
| 目前许多力学问题,如计算物理、地质学、结构设计、分子光谱学、电学、参数识别、自动控制、商务智能、线性
系统理论、大数据分析与动态分析等领域,都要依赖于矩阵方程。 研究了矩阵方程 AX = B 的求解问题,给出了矩
阵方程 AX = B 有解的新判别条件及其通解表达式,推广了矩阵方程 AX = B 的判解条件和通解形式;例题表明简化
了矩阵方程 AX = B 的求解过程,同时也简化了向量组的线性表示式和基到基的过渡矩阵计算,这对于充实矩阵方
程的求解理论和简化计算均是有益的。 |
| 关键词: 初等变换 矩阵方程 通解 线性表示 过渡矩阵 |
| DOI： |
| 分类号: |
| 基金项目: |
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| Solutions to a Class of Matrix Equations and Their Applications |
|
FANG Jianwei YUAN Huiping
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School of Software Chongqing Finance and Economics College Chongqing 401320 China
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| Abstract: |
| Matrix equations are crucial in solving many problems in various fields such as mechanics computational
physics geology structural design molecular spectroscopy electrical engineering parameter identification automatic
control business intelligence linear system theory big data analysis and dynamic analysis. This study investigates the
solution of the matrix equation AX = B providing new criteria for the existence of solutions and their general expressions.
It extends the conditions for solvability and the general forms of the solutions of the matrix equation AX = B. Examples
demonstrate that this approach simplifies the solution process of the matrix equation AX = B as well as the calculation of
linear representations of vector sets and the transition matrix between bases. This contributes to enriching the solution
theory of matrix equations and simplifying computations. |
| Key words: elementary transformations matrix equations general solution linear representations transition matrix |
