弱正交补的唯一性及其应用

The Uniqueness of Weak Orthogonal Complement and Its Applications

在一般的线性空间中引入弱内积,使之成为弱内积空间,再引入弱正交、弱正交补概念,证明了任何数域上的线性空间都是弱内积空间、任何弱内积空间的子空间都有唯一的弱正交补,并给出了齐次线性方程组同解的一个充分必要条件。

By introducing first the concept of weak inner and weak orthogonal complement, we have testified the uniqueness of weak orthogonal complement and finally give the necessary and sufficient condition for the same solution of the homogeneous linear equations.