次正交矩阵
摘 要
本文主要对次正交矩阵、向量的次正交、次正交规范基、次正交变换及子空间的次正交等内容作了一些探讨。对照正交矩阵讨论了次正交矩阵的性质，总结出了一个有关向量与自身次正交的结论。进一步地，给出了n维欧氏空间Rn中次正交规范基和次正交变换的定义，并且得到了次正交规范基及次正交变换的一些重要性质。最后，参照空间正交的定义，给出了子空间次正交的定义，并得出了一些结论。
关键词：次正交矩阵，次正交规范基，次正交变换，子空间的次正交
ABSTRACT
In this paper, some contents about sub-orthogonal matrix, sub-orthogonal vectors,
sub-orthogonal normalized basis, sub-orthogonal transformations and sub-orthogonal subspace are discussed mostly. According to orthogonal matrix, we discuss the properties of sub-orthogonal matrix. And we also draw a conclusion about the sub-orthogonality between vector and itself. What’s more, we give the definitions of sub-orthogonal normalized basis and sub-orthogonal transformations in n-dimension Euclidean space Rn. And some important properties of sub-orthogonal normalized basis and sub-orthogonal transformations are gained, too. Finally, we obtain the definition of sub-orthogonal subspace and some conclusions referring to the orthogonal subspace.
Key words: sub-orthogonal matrix, sub-orthogonal normalized basis, sub-orthogonal
transformations, sub-orthogonal subspace
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目 录
摘 要 .............................................. I ABSTRACT ............................................. II 0 引言 ................................................... 1 1 预备知识 ...............................................................................................1 1.1 常用符号和基本定义..........................................................................................1 1.2 基本引理 ....................................................................................................................2 2 正交矩阵的性质.....................................................................................2 2.1 正交矩阵的定义.....................................................................................................2 2.2 正交矩阵的性质......................................................................................................3 3 次正交矩阵..............................................................................................3 3.1 次正交矩阵的定义..................................................................................................3 3.2 次正交矩阵的性质..................................................................................................4 4 欧氏空间的次正交变换及其性质..........................................................10 4.1 次正交规范基............................................................................................................10 4.2 次正交变换..................................................................................................................13 5 子空间的次正交......................................................................................15 参考文献......................................................................................................17
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