Research On The Inequality Of Harmony And Magic Array

The research content of matrix inequalities is vast.Among them,the inequality of positive semi-definite Hermite matrix trace has an indispensable and unique position in matrix theory,and has made outstanding contributions to the improvement of the matrix inequality system.The inequality of the magic matrix and the magic matrix is one of the matrix inequalities.This is a special situation and has not yet begun to dig into and study in depth,and there is a lot of content worth discussing and learning.This article will describe and study the inequality of the phantom from these four perspectives.First,it introduces the definition of six kinds of magic arrays: row and magic array,column and magic array,weak and magic array,accumulated magic array and he accumulated magic array.Secondly,according to the nature of the calculation of the matrix and the magic matrix is a special matrix analogy,the traces of the magic matrix,the trace of the product magic matrix,and the trace of the product magic matrix are obtained;the definition of three magic matrix traces The main study is the trace and related properties of the sum magic matrix under the Hadamard product.Then use the method of matrix identity deformation,the inequality of the Hermite semi-positive semi-definite matrix trace,and the trace analogy of the Hadamard product to the magic matrix to verify and generalize the inequality of the magic matrix under the Hadamard product.Finally,according to the inequality of the matrix under the general product,the connection between the magic matrix and the matrix,and the analogy of the operational properties of the magic matrix,the inequality of the magic matrix under the general product is obtained.