n阶方阵的m次方根

n阶方阵的m次方根

摘 要：在本文中，作者首先利用Cayley-Hamilton 定理讨论2阶方阵在什么情况下有平方根，若有的话，有多少，并且如何去求出其全部平方根；然后利用2阶方阵的Jordan标准型给出2阶方阵的所有 次方根；最后给出了复数域内n阶方阵存在m次方根的充分条件.

关键词：复数域；2阶方阵；平方根；Jordan标准型； n阶矩阵的m次方根

The m-th Roots of Square Matrices of Degree n

Abstract: In this paper,firstly,the author uses Cayley-Hamilton’ theorem Üto discuss the 2-th rooมts of square matrices of degree 2, if the 2-th roots of square matrices exist,the author will give all 2-th roots of square matrices of degree 2 .Secondly,by using the Jordan form of square matrices,the author gives all -th roots of square£ matrices of degree 2.Lastly, the paper presents the sufficient conditions of the existence of -th roots of square matrices of degree n.

Key words：Plural field; Square matrices of degree ℉2; Square roots; Jordan form; -th roots of square matrices of degree n．