The Study On Properties Of Adjoint Matrix

Adjoint matrix is a basic concept in the matrix theory and linear algebra,and it is an important tool to study many problems of mathematics.As a special matrix,the theory and the application of adjoint matrix have it's own character.Adjoint matrix is only a tool to colculate inverse matrix during college mathematics.In this paper,we study properties of adjoinnt matrix from different sort,discuss the proof of these properties and get some significative conclusions.(1)To introduce some basic properties of adjoint matrix in determinant and rank;(2)To study some properties of operation on adjoint matrix of multiple matrix, multiplicative matrix,block matrix and some properties of operation on inverse of adjoint matrix(3)To study the association properties of adjoint matrix.Positive-definitenss, symmetry,singularity,orthogonality of adjoint matrix are given by positive-definitenss, symmetry,singularity,orthogonality of matrix;(4)To study the properties of relations between different adjoint matrices in this part.To give similarity and congruence of adjoint matrix;(5)To study some properties about characteristic value and characteristic vector;(6)To give a definition and a form of m- adjoint matrix,and to study some proper-ties of m-adjoint matrix.In this paper,the study on some properties of one kind of block matrix is creative point.