| 用正交变换化实二次型为标准形的同步求解问题 |
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| 引用本文： | 李延敏,张力.用正交变换化实二次型为标准形的同步求解问题[J].大学数学,2011,27(5):167-171. |
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| 作者姓名： | 李延敏 张力 |
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| 作者单位： | 1. 吉林财经大学应用数学学院,长春,130117
2. 东北师范大学物理学院,长春,130024 |
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| 基金项目： | 吉林省教育科学“十一五”规划重点项目，吉林省教育厅重点教研项目，吉林省自然科学基金项目 |
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| 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.
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| 关 键 词： | 二次型 标准形 互逆变换 正交变换 同步求解 |
The Synchronization Solution of Transforming the Real Quadratic Forms into the Canonical Forms with Orthogonal Transformation |
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| LI Yan-min,ZHANG Li.The Synchronization Solution of Transforming the Real Quadratic Forms into the Canonical Forms with Orthogonal Transformation[J].College Mathematics,2011,27(5):167-171. |
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| Authors: | LI Yan-min ZHANG Li |
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| Institution: | LI Yan-min1,ZHANG Li2(1.School of Applied mathematics,Jilin University of Finance and Economics,Changchun 130117,China,2.School of Physics,Northeast Normal University,Changchun 130024,China) |
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| Abstract: | 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. |
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| Keywords: | quadratic forms canonical forms reciprocal transformation orthogonal transformation synchronizedsolution |
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