反对称线性变换与Gram-Schmidt正交化  

Anti-symmetrical Linear Change and Gram-Schmidt Orthogonalization Process

作　　者：刘妍珺[1] 马赞甫[2] 余孝军[1] LIU Yan-jun;MA Zan-fu;YU Xiao-jun(School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025 China;Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics Guiyang 550025, China)

机构地区：[1]贵州财经大学数学与统计学院,贵州贵阳550025 [2]贵州财经大学贵州省经济系统仿真重点实验室,贵州贵阳550025

出　　处：《数学的实践与认识》2018年第9期285-289,共5页Mathematics in Practice and Theory

基　　金：教育部人文社会科学基金项目(12YJC790140);国家留学基金委西部项目(201608525051);国家自然科学基金(71761005)*通信作者

摘　　要：利用反对称矩阵可实施反对称变换，将任意非零向量转变为与之正交的向量．基于这一考虑，可对给定向量组实施反对称线性变换，将其转化为一个与之等价的正交向量组．该种线性变换从另一角度解释了Gram—Schmidt正交化．The anti-symmetric variation can be implemented by using the antisymmetric matrix, and any nonzero vector is transformed into a vector that is orthogonal to it. Based on this consideration, an anti-symmetric change is applied to a given vector group, and an equivalent orthogonal vector group is obtained. The anti-symmetrical linear change explains the Gram-Schmidt orthogonalization from another perspective.

关 键 词：反对称矩阵 反对称变换 Gram-Schmidt正交化 

分 类 号：O151.21[理学—数学]