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  DOI Prefix   10.20431


 

International Journal of Scientific and Innovative Mathematical Research
Volume 7, Issue 8, 2019, Page No: 3-7

The Inequalities of Positive Semi-Definite Block Matrix with Partial Order Relations

Hui Quan*

Department of mathematics, Northeast Forestry University, Harbin, China,150040.

Citation : Hui Quan, The Inequalities of Positive Semi-Definite Block Matrix with Partial Order Relations International Journal of Scientific and Innovative Mathematical Research 2019 , 7(8) : 3-7.

Abstract

This paper, we firstly do the same thing for a 3 X 3 positive semi-definite block matrix, and give a generalization of the above theorem. Next, we further generalize the case of k X k positive semi-definite block matrix, and discuss the partial ordering relationship between the sum of matrices on quasi-diagonal lines and block matrices at other locations. Thus, we gave a new eigenvalue inequality.


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