广义共轭延拓矩阵的奇异值分解

Singular Value Decomposition for Generalized Conjugated Extended Matrix

定义广义共轭延拓矩阵的概念,利用复矩阵的实分量矩阵,分别建立广义行共轭延拓矩阵和列共轭延拓矩阵与其母矩阵的实分量矩阵的奇异值和奇异向量之间的定量关系.所得行或列延拓矩阵的奇异值等于母矩阵的实分量矩阵奇异值的2^(1/2)倍,相应的右或左奇异向量矩阵是实正交矩阵.

The generalized conj ugated extended matrix is defined in this paper.By employing real component matrices of a complex matrix,some quantitative correspondences of the singular values and singular vectors between the row or column generalized conj ugated extended matrix and the real component matrices of their original matrix are derived,where the singular values of the row and column extended matrices are equal to √2 times of those of the real component matrices of the original matrix and corresponding matrices formed by right and left singular vectors are real orthogonal matrices,respectively.