关于正交变换的判定

DECISION OF ORTHOGONAL TRANSFORMATION

于欧氏空间的变换是正交变换的判定 ,杨子胥给出了一个充要条件 ;吴有为给出了三个充要条件 ;本文又给出了一个充要条件 ,推广了吴有为的定理并简化了他的证明 ,同时削弱了张禾瑞编高等代数 (第三版 )§ 8.4习题

Yang Zixu gave a necessary and sufficient condition for transformation on Euclidean space to be orthogonal. Wu Youwei also gave three conditions about it. In this paper, the author gives further eleven necessary and sufficient conditions, which extend Wu's theorem, and simplify his proof. In the meanwhile, these conditions weaken the condition of a theorem in §8.4 excercise 1 of 《Higher Algebra》 written by Zhang Herri and the condition of a theorem in [5].