本文从普通奇异值分解出发 ,导出了具有行或列对称结构的矩阵 (即延拓矩阵 )的奇异值和奇异向量与原矩阵 (亦称母矩阵 )的奇异值和奇异向量的定量关系 ,并对延拓矩阵进行了简单的扰动分析 .理论分析和数值实验的结果表明 ,就一大类延拓矩阵而言 ,仅用母矩阵进行奇异值分解不但可以节省计算量和存储量 ,而且不影响任何数值精度 Starting from the general singular value decomposition, this paper deduces the quantitative relationship between the singular value and the singular vector of the matrix with row or column symmetry structure (ie, extension matrix) and the singular values ​​and singular vectors of the original matrix (also known as the matrix matrix) The simple perturbation analysis of continuation matrix is ​​carried out.The theoretical analysis and numerical experiments show that in the case of a large continuation matrix, singular value decomposition using only mother matrix can not only save computation and storage but also have no effect Any numerical accuracy