淮北师范大学学报：自然科学版
淮北師範大學學報：自然科學版
회북사범대학학보：자연과학판
Journal of Huaibei Coal Industry Teachers College(Natural Science edition)
2012年
4期
17-21
,共5页
矩阵%P-若当块%P-若当形矩阵%特征多项式%最小多项式%不变子空间
矩陣%P-若噹塊%P-若噹形矩陣%特徵多項式%最小多項式%不變子空間
구진%P-약당괴%P-약당형구진%특정다항식%최소다항식%불변자공간
matrix%P-Jordan block%P-Jordan standard form matrix%characteristic polynomial%minimal polynomial%invariant subspace
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.
文章證明瞭一般數域P上方陣A都相似于P-若噹形矩陣.在P=C時它就是若噹標準形,P-若噹形矩陣可看成複數域上若噹標準形的推廣,是若噹標準形與有理標準形的結閤.利用P-若噹形矩陣給齣瞭n維線性空間V的線性變換有有限箇不變子空間的充要條件.
문장증명료일반수역P상방진A도상사우P-약당형구진.재P=C시타취시약당표준형,P-약당형구진가간성복수역상약당표준형적추엄,시약당표준형여유리표준형적결합.이용P-약당형구진급출료n유선성공간V적선성변환유유한개불변자공간적충요조건.
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.
