从几道考研题谈线性变换与矩阵命题的转化  

From Several Postgraduate Entrance Examination Questions to Conversion between Linear Transformation and Matrix

作　　者：尹小艳 施德才 YIN Xiaoyan;SHI Decai(School of Mathematics and Statistics, Xidian University, Xi’an 710071, China)

机构地区：[1]西安电子科技大学数学与统计学院,陕西西安710071

出　　处：《河南教育学院学报（自然科学版）》2022年第2期55-59,共5页Journal of Henan Institute of Education(Natural Science Edition)

基　　金：西安电子科技大学矩阵分析与计算精品课程建设项目。

摘　　要：对几道抽象难解的线性变换考研题给出了简洁的矩阵证明,并由此深入讨论了线性变换与矩阵命题的转化,强调了高等代数教学中问题转化意识的培养和能力的提升。The elegant correspondence relationship between linear transformation and matrix is discussed in detail first.Then based on this relationship,several abstract problems on linear transformation are solved concisely by transforming them to their corresponding matrix questions.The mathematical idea of converting complex and abstract concepts to simple and concise objects,as well as several other important mathematical ways of thinking,are emphasized.

关 键 词：线性变换 矩阵 同构 正交变换 正交矩阵 

分 类 号：O151.2[理学—数学]