准正交变换的三种等价定义及其判定

摘要

从正交变换的定义形式以及几何意义上推广了正交变换的定义,并证明了三种推广定义的等价性,将推广后的线性变换称为准正交变换,同时指出了参考文献[5]中推广正交变换时存在的一个重大问题.探讨了准正交变换的一系列性质和判定法.%The definition of orthogonal transformation is promoted in the form of definition as well as in the geometric significance, and the equivalence of the there promoted definitions is proved. The promvted linear transformation is called almost-orthogonal transformation. The article also points out a big problem of References [5] in the promotion of orthogonal transformation. Properties and the determination method of almost-orthogonal transformation are discussed.