正定矩阵的算术平方根  

Arithmetic Square Root for Positive Definite Matrixes

作　　者：张姗梅[1] 刘雁[2] 

机构地区：[1]太原师范学院数学系,山西太原030012 [2]黑龙江大学数学科学学院,黑龙江哈尔滨150080

出　　处：《高等数学研究》2012年第1期10-13,共4页Studies in College Mathematics

基　　金：山西省重点学科资助项目(2009021)

摘　　要：对正定矩阵的算术平方根的唯一性进行探讨.根据Lagrange插值多项式以及可逆矩阵的唯一分解性,用两种方法证明正定矩阵的算术平方根是唯一的,并通过实例说明正定矩阵的算术平方根的求法及应用.In this note, the uniqueness of the arithmetic square root for a positive definite matrix is discussed. Ifs proved that the arithmetic square root is unique in two ways, by the virtue of the Lagrange interpolation polynomial and by using the result of every inverse matrix can be uniquely decompose to the product of an orthogonal matrix with a positive definite matrix. In the end, some examples are given to illustrate the method of finding the arithmetic square root of a positive definite matrix.

关 键 词：正定矩阵 特征值 正交矩阵 

分 类 号：O151.21[理学—数学]