摘要
恰当的反例能很好地帮助学生正确地理解和掌握相关数学概念及定理.本文研究了高等代数中有关矩阵、多项式和线性变换中的典型问题,并通过修改命题的条件或结论构造了反例,深入探讨了特殊矩阵及其联系、多项式的整除性等方面的命题.高等代数的反例研究对于高等代数教学具有较好的指导意义.
The proper counterexamples can help the students to understand and grasp the mathematic concepts and the theories. In this paper, the typical questions about matrices, polynomial and linear transformation in the advanced algebra were researched. Some counterexamples were constructed by changing the conditions and conclusions,and special matrices and their connections, polynomial divisi- bility were further studied. The research about the counterexamples has a better aignificance for higher algebra teaching.
出处
《甘肃联合大学学报（自然科学版）》
2012年第4期93-95,共3页
Journal of Gansu Lianhe University :Natural Sciences
基金
安徽省教育厅教学研究项目(20101071)
宿州学院智能信息处理实验室开放课题(2010YKF12)
宿州学院教学研究项目(szxyjyxm201143)
关键词
反例
矩阵
多项式
线性变换
eounterexample
matrix
polynomial
linear transformation
