自伴矩阵与Hermite二次型  

Independent companion matrix and Hermite quadratic form

作　　者：杜鹃[1] 范啸涛[1] 杨建康[1] 

机构地区：[1]成都理工大学信息管理学院,成都610059

出　　处：《成都理工大学学报（自然科学版）》2007年第4期478-481,共4页Journal of Chengdu University of Technology: Science & Technology Edition

摘　　要：通过对自伴矩阵的深入分析和讨论,给出了自伴矩阵的特征值及特征向量的性质;证明了自伴矩阵一定可以酉相似于对角阵;得到了Hermite二次型可通过可逆线性变换化为标准形的一般方法以及Hermite二次型正定的几个充要条件。Based on a through analysis and discussion of independent companion matrix, this paper presents the properties of the characteristic value and the characteristic vector of independent companion matrix. It provides the proof that independent companion matrix is unitary congruent with a opposite angles matrix. It presents the general method to transform the Hermite quadratic form into the standard form based on the contrary line transformation, and provides several necessary and sufficient conditions of the positive Hermite quadratic form.

关 键 词：自伴矩阵 HERMITE矩阵 复二次型 

分 类 号：O151.21[理学—数学]