Arithmetic Square Root for Positive Definite Matrixes
Yan Liu · Studies in College Mathematics · 2012
In this note,the uniqueness of the arithmetic square root for a positive definite matrix is discussed.It's 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.