有限维欧氏空间中内积问题的矩阵研究

THE MATRIX STUDY OF THE ORTHOGONAL COMPLEMENT IN FINITE DIMENSIONAL EUCLIDAN SPACE

利用向量组的Gram矩阵和向量的坐标矩阵对有限维欧氏空间中子空间的正交性给出了矩阵判定条件,对子空间的正交补及向量在子空间上的内射影给出了矩阵表示.获得了一些简捷有用的结果。

In this paper, some decision theorems are suggested about the matrix orthogonal problem on the subspace of the finite dimensional Euclidan subspace. In addition, some concise results are obtained by matrix representation of the orthogonal complement and injection of vectors on the subspace.