一般数域P上方阵的标准形

Standard Form of Square Matrix on the General Number Field

文章证明了一般数域P上方阵A都相似于P-若当形矩阵.在P=C时它就是若当标准形,P-若当形矩阵可看成复数域上若当标准形的推广,是若当标准形与有理标准形的结合.利用P-若当形矩阵给出了n维线性空间V的线性变换有有限个不变子空间的充要条件.

Firstly the result that the matrix of order n on the general number field P must be similar to its PJordan standard form is accomplished.When P = C,P-Jordan standard form is Jordan standard form,viewed as the extension of Jordan standard form of complex field,is the combination of Jordan standard form and rational canonical form.Then the necessary and sufficient conditions that the linear transformation of linear space of dimension n has limit invariant subspaces are concluded by using P-the Jordan standard form.