再谈初等变换法在矩阵计算中的应用_英文_.pdfVIP

2008 年第 3 期 重庆三峡学院学报 No.3.2008 第 24 卷（110 期） JOURNAL OF CHONGQING THREE GORGES UNIVERSITY Vol.24 No.110 Re-discussing Applications of Elementary Transformation in Matrix computation FENG Tian-xiang (College of Mathematics and Computer Science, Chongqing Three Gorges University, Wanzhou Chongqing 404000) Abstract: In matrix computation, calculating eigenvalues and diagonalizing matrix are key work. The QR decomposition of a matrix is a useful tool in matrix computation. But the process of QR decomposition is very complex. An elementary transformation method for diagonalizing matrices and factorizing matrices in QR form is derived. At last, QR decomposition of a matrix is given by using triangular factorizations. Key words: Eigenvalue; Diagonalization; Elementary transformation; QR decomposition. CLC number: O175.9 Document code: A Article numbe r:1009-8135（2008）03-0061-03 1 Introduction Usually, for an n ×n matrix over a number field F , eigenvalues are obtained by solving its eigenequation. That is to say, we need to solve an equation of order n in one variable, whose processing is very trouble. Similarly, if we diagonalize a matrix A , we need to judge whether A has n linear independent eigenvectors; if similar transformation matrix is required, we have to find basic solutions of a system of n linear equations in n variables. The QR decomposition of a matrix is one of the useful methods in matrix computation. But its computing process is very complex, which makes us trouble. In this paper, we give an e