An elementary proof of arithmetic-geometric mean inequality of the weighted Riemannian mean of positive definite matrices

作者：Yamazaki Takeaki^*

来源：Linear Algebra and Its Applications, 2013, 438(4): 1564-1569.

DOI：10.1016/j.laa.2011.12.006

• Positive definite matrix
• Geometric mean
• The Riemannian mean
• Matrix inequality
• Arithmetic-geometric mean inequality

The weighted Riemannian mean of positive definite matrices is a kind of weighted geometric mean of n matrices. Some properties of the weighted Riemannian mean are easily obtained. But some of them are not easy. In this short paper, a simplified proof of arithmetic geometric harmonic mean inequalities will be obtained.

• 出版日期2013-2-15