复向量空间的分解与复线性变换的Jordan标准形*

本文引入表征复线性变换结构的新对象。这些新对象给出复向量空间关于复线性变换分解的新结果且给出构造Jordan标准形的所有Jordan基。因而,它们能够直接导致着名的Jordan定理及空间的第三分解定理,且能给出对Jordan形精致微妙结构的新的深刻洞察。后者表明,复线性变换的Jordan标准形是一种在双重任意选择下具有不变性的结构。

On the Decomposition of Complex Vector Spaces and Jordan Canonical Form of Complex Linear Transfomations

New objects characterizing the structure of complex linear transformations are introduced.Tbese new objects yield a new result for the decomposition of complex vector spaces relative to complex linear transformations and provide all Jordan bases by which the Jordan canonical form is constructed.Accordingly,they can result in the celebrated Jordan theorem and the third decomposition theorem of space directly and, moreover,they can give a new deep insight into the exquisite and subtle structure of the Jordan form. The latter indicates that the Jordan canonical form of a complex linear transformation is an invariant structure associated with double arbitrary choices.