正定矩阵的算术平方根

Arithmetic Square Root for Positive Definite Matrixes

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.