The Inequalities of Positive Semi-Definite Block Matrix with Partial Order Relations
Hui Quan*
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.
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.