Jordan标准形教学的一点思考

摘要

近年来无线维代数和无限维表示理论的研究逐渐成为代数研究的热点。从教学实践上来讲，在高等代数课程教学中注意相关结论的证明方法对学生理清哪些结论并不完全依赖于向量空间是有限维这一条件是很有帮助的。本文从Jordan标准形的证明处理方法出发，做了一点尝试。%The infinite dimensional algebras and the infinite di-mensional representation theory have become one of the most at-tractive areas in algebraic research in recent years. From the as-pect of teaching practice, it is helpful for students to clarify whether a result is dependent on the finite dimensional condition or not provided by the teacher might supply a nice way to state and prove it. In this paper, as an example, we give a new proof of the classical result of Jordan canonical form which also works for infinite dimensional case.