| 关于正交变换可对角化的充要条件 |
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| 引用本文： | 袁辉坪.关于正交变换可对角化的充要条件[J].西华师范大学学报(哲学社会科学版),1997,18(1):37-41. |
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| 作者姓名： | 袁辉坪 |
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| 作者单位： | 渝州大学数学系 |
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| 摘 要： | 给出了丰交变换和正交矩阵可对角化的一系列充要条件，推广了张禾瑞，郝炳新所著高等代数中的一个例题和张远达的线性代数原理中一个定理；并对张慧敏，张宪君的正交变换可对角化的一个充要条件一文的定理１，定理２作了完善和推广。获得了一种求可对角化正交矩阵的特征向量的简便方法。
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| 关 键 词： | 正交变换 正交矩阵 可对角化 充要条件 欧氏空间 |
THE NECESSARY AND SUFICIENT CONDITIONS FOR DIAGONALIZABLE ORTHOGONAL TRANSFORMATION |
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| Abstract: | A series of necessary and sufficient conditions for the diagonalizable orthogonal transformation and orthogonal matrix are given.Under these conditions the paper develops a proposition in Higher Algebra written by Zhang Herui and Hao Binxing and a theorem in Linear Algebra written by Zhang Yuanda,and completes an important condition proposed by Zhang Huiming and Zhang Xianjun for diagonalizable orthogonal transformation:Theorems 1 and 2.Thereby a simple and convenient method for computing the characteristic vector of diagonalizable orthogonal matrix is attained. |
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| Keywords: | orthogonal transformation orthogonal matrix diagona lizable necessary and sufficient condition |
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