实对称矩阵对角化的研究  

Research on Diagonalization of Real Symmetric Matrix

作　　者：鲁琦[1] 刘钢 LU Qi LIU Gang(Department of Mathematics and Physics, Bengbu University, Bengbu 233030, China School of Mathematics and Statistics, Suzhou University, Suzhou 234000, China)

机构地区：[1]蚌埠学院数学与物理系,安徽蚌埠233030 [2]宿州学院数学与统计学院,安徽宿州234000

出　　处：《佳木斯大学学报（自然科学版）》2016年第5期834-836,共3页Journal of Jiamusi University：Natural Science Edition

基　　金：安徽省数学与应用数学专业改革项目(2014zy141);蚌埠学院工程化教学研究项目(2013gcjy17);蚌埠学院自然科学研究一般项目(2015ZR10)

摘　　要：若实对称矩阵可对角化,则存在正交矩阵,使其相似于对角矩阵,且正交矩阵的选取不是唯一的。探讨了实对称矩阵正交对角化过程中选取的正交矩阵之间的关系,并举例说明。If a real symmetric matrix was diagonalizable, then there existed an orthogonal matrix which can make the real symmetric matrix similar to a diagonalization matrix, and the real symmetric matrix was not u-nique.We discussed the relationship between the orthogonal matrices in the process of orthogonal diagonalization of real symmetric matrix, and an example was given to explain it.

关 键 词：矩阵 对角化 正交矩阵 

分 类 号：O153.3[理学—数学]