Study on the blocking and application for matrix
Gao Zhen-xing · Journal of Liaoning Normal University · 2011
This paper makes use of the conclusion of I product A≥0,B≥0A+B≥0 and II product A≥0,B≥0AB≥0.Where the matrix A is positive semi-definite when A≥0,AB=(aijbij) is the Hadamard product of matrix A and B.These two conclusions show that: Let L be dual function class,for arbitrary f∈L,(ABB*C)≥0|f(B)|2≤f(A)f(C),the element in class L is determinant,trace,unitarily invariant norm and so on.We use this theorem as a tool,and illustrate the use of block matrix method in matrix inequalities and linear map by giving instances.