The Dissolution Of Matrix On Field And Solid

The dissolution of matrix is to decompose a matrix into several rather simple matrixes through changes or a profuct of some matrix with certain special characters.The dissolution theory of matrix is of great importance both to the theory of matrix and numerical value calculation.lt is also widely used is the field of engineering technology,such as machine and structure,the control of the posture of man-made satellite and the identification system.This paper deals with the matrix dissolution in the complex number(number) field and the quaternion,and the dissolution and use of some product form in the invertible matrit.The main content of the paper is as the following:1.The rank decomposition and full rank decomposition of matrit in any numerical field;the result is that any complex matrit can be dissoluted into a two-Antisymmetric-matrix's product.and one is invertible Antisymmetric matrix.2.The dissolution of some product forms of real matrix and invertible matrix is mentioned in the paper.The result is that any n-order invertible matrix can be dissoluted into a product of a positive Negative definite matrix and an orthogonal matrix,and the factorization is the only.3.The paper deals with the similar to the standard model of the orthogonal matrix,too.It gives n dimensional euclidean space(n≥2),and it shows that any orthogonal transformation in V can be expressed as the specular reflection of the plot of a number(≤n).4.It points out the UDL dissolution of the matrix in the quaternion and the dissolution of quaternion matrix which can be centralized.The singular value deomposition of the matrix has been popularized to quaternion.