矩阵的初等变换及其应用（Elementary transformation of matrix and its application）.docVIP

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矩阵的初等变换及其应用（Elementary transformation of matrix and its application）.doc

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矩阵的初等变换及其应用（Elementary transformation of matrix and its application）

矩阵的初等变换及其应用（Elementary transformation of matrix and its application） Elementary transformation of matrix and its application Wang Dan Elementary transformation of matrix and its application Abstract Elementary transformation of matrix is an important method of studying matrix, and it is the core of application in linear algebra. This paper introduces some concepts and properties associated with the matrix, on the basis of matrix rank, the basis for judgment matrix is invertible, after inverse matrix equations, eigenvalues and eigenvectors, two types of standard form, and illustrate the application of elementary transformation of matrix in the above is how to play the role of. Keywords: matrix, elementary transformation, application The, elementary, transformation, of, matrix, and, its, applications Abstract Elementary transformation matrix is an important means of Matrix is the core linear algebra applications. This article briefly describes some of the concepts and properties associated with the matrix as a basis, the rank of a matrix to determine whether a matrix is reversible after inverse matrix, seeking basic solutions line equations find eigenvalues, and eigenvectors, quadratic standard Shape and so on. Illustrate the elementary transformation matrix in the above applications is how to play a role. Keywords:, matrix, elementary, transformation, application Catalog 1. introduction 6 2. the related concepts of matrix 7 2.1 definition of matrix 7 2.2 transpose of matrix 7 2.3 elementary transformation of matrix and elementary matrix 7 3. the application of elementary transformation of matrix 8 3.1, the rank of the matrix 8 3.2 the inverse matrix of the matrix 10 3.3 using elementary transformation to solve matrix equation 11 3.4 find the solution of linear equations 12 The conditions for the existence of nonzero solutions of 3.4.1 homogeneous linear equations are 13 Conditions for the existence of solutions of 3.4.2 nonhomogeneous linear equations 14 3.5 find the