欧氏空间的广义次对称变换  

The Euclidean Space Secondary Generalized Symmetry Transformation

作　　者：危琼[1] 冯茂春[1] 

机构地区：[1]湖州师范学院理学院,浙江湖州313000

出　　处：《湖州师范学院学报》2009年第1期135-140,共6页Journal of Huzhou University

基　　金：湖州师范学院教改重点项目(2008JY006)

摘　　要：在广义次对称矩阵定义的基础上,利用双线性函数这一工具,给出欧氏空间的广义次对称变换的概念,并利用它与广义次对称矩阵的关系,探讨了广义次对称变换的相关性质:线性性质和乘积和特征值.然后进一步给出相关的次正交和次正交补的概念,并研究次正交向量组的线性无关性、次正交向量组与次正交基的关系以及次正交补的存在性等性质.最后给出具体的例子加以说明.This paper gives the definition of the Euclidean space generalized secondary symmetry transformation on the basis of the definition of the generalized secondary symmetrical matrix and the bilinearity, discuses the related properties of the Euclidean space generalized secondary：linearnature,product,eigenvalue function according to the relationship between the generalized secondary symmetrical matrix and the euclidean space of generalized secondary symmetrical transformation, gives the concept of the orthogonation and the orthogonal complement, studies their properties ： linear independence, their relation, the existence and unicity of the orthogonal Complement, etc. , and finally illustrates the problem.

关 键 词：次对称双线性函数 次正定双线性函数 次对称矩阵 次正定矩阵 广义次对称变换 

分 类 号：O151.21[理学—数学]