无限维欧氏空间的子空间的正交补

Orthogonal Complement for Subspace in Infinite Eucliden Space

文章利用标准正交基,证明了无限维欧氏空间的有限维子空间都有唯一的正交补.并进一步证明若无限维欧氏空间的有限维子空间是某正交变换的不变子空间,则其正交补也是该正交变换的不变子空间,但对无限维子空间结论不成立.

The fact that each finite subspace has a unique orthogonal in an Eucliden space is proved in virtue of standard orthogonal basis. Further,the orthogonal complete of a finite subspace respects the invariant for a linear transformation is proved,and it doesn＇t hold for infinite subspace.