摘要
作为《关于矩阵的特征值与特征向量同步求解问题》的续篇,利用其给出的方法,证明了新的定理.通过对实对称矩阵进行行列互逆变换,同步求出二次型的标准形及正交变换阵,简化了复杂的施密特正交化法,较好地解决了二次型标准形与正交变换阵同步求解问题.
As the sequel of the paper ＂On the Cogradient Solving Question of Eigenvalue and Eigenvector of a Matrix＂, in this paper, the author proved new theorems with the use of the methods given in the paper. Through carrying on reciprocal transformation of the rows and columns to the real symmetric matrix, the author obtained the standard forms and the orthogonal transformation matrix of the quadratic forms simultaneously, simplified the complex Schmidt orthogonalization method and solved well the synchronization solution problem of the canonical forms and the orthogonal transformation matrix of the auadratic forms.
出处
《大学数学》
2011年第5期167-171,共5页
College Mathematics
基金
吉林省教育科学"十一五"规划重点项目(ZC0148)
吉林省教育厅重点教研项目(吉高教字[2008]41号2008193)
吉林省自然科学基金项目(20101599)
关键词
二次型
标准形
互逆变换
正交变换
同步求解
quadratic forms
canonical forms reciprocal transformation
orthogonal transformation synchronizedsolution
