Some results on the partial orderings of block matrices

Abstract

Abstract Some results relating to the block matrix partial orderings and the submatrix partial orderings are given. Special attention is paid to the star ordering of a sum of two matrices and the minus ordering of matrix product. Several equivalent conditions for the minus ordering are established. Mathematics Subject Classification (2000): 15A45; 15A57

Keywords

• Matrix partial orderings
• Moore-Penrose inverse
• Block matrix