矩阵多项式的逆矩阵求解方法  

Inverse Matrix Solution of Matrix Polynomial

作　　者：蔡学鹏 Cai Xuepeng(College of Mathematics and Physics,Xinjiang Agricultural UniversityXinjiangUrumqi830052)

机构地区：[1]新疆农业大学数理学院,新疆乌鲁木齐830052

出　　处：《科技风》2024年第14期25-27,共3页

基　　金：新疆农业大学教研教改项目“融入人工智能元素的《线性代数》课程的教学案例设计”,项目编号:2024PTJG092。

摘　　要：矩阵多项式理论知识在很多线性代数或者高等代数教材中都有所涉及,其逆矩阵求解计算性较强,方法较多。本文主要概述了不同矩阵多项式的逆矩阵的各类求解方法,即:多项式除法、待定系数法、替代法、综合除法.教师在课堂教学中适当地融入本文内容作为素材,可以深化教学内容,增强知识点之间的关联性,也能培养学生探索知识点间相互渗透的主动意识,对培养学生创新意识、创新能力,提高学生学习线性代数和高等代数课程的主动性有着重要的作用.The knowledge of matrix polynomial is involved in many linear algebra textbooks,and its inverse matrix solution is more computationally efficient and has many methods.In this paper,various methods of solving the inverse matrix of different matrix polynomials are summarized,namely:polynomial division,undetermined coefficient method,alternative method,synthetic division method.If teachers properly integrate the content of this paper into the classroom teaching as materials,it can deepen the teaching content,enhance the correlation between knowledge points,and cultivate students'active awareness of exploring the mutual penetra-tion of knowledge points,which plays an important role in cultivating students'innovation awareness and innovation ability and im-proving students'initiative in learning linear algebra and advanced algebra courses.

关 键 词：逆矩阵 多项式除法 待定系数法 替代法 综合除法 

分 类 号：G642[文化科学—高等教育学]