域上线性变换标准型的构造

The Construction of Canonical Form for Linear Transformation on Field

所研究的域上线性变换的标准型具有直接反映初等因子和不变因子等不变量这一特点。给出了域上线性变换某一类标准型能被构造出来的充要条件,并具体构造出了这一类中的三种新标准型,使得其中一种是第一有理标准型和第二有理标准型以及Jordan标准型的统一形式。

A sufficient and necessary condition is derived for the construction of a class of canonical form for linear transformation on field,and a few concrete examples are obtained. Further more,it is the aim of this paper to present a new coanonical form to unify the known forms：the first and the second rational canonical form,the Jordan canonical form and the canonical form on real field.