奇异值分解及其简单应用

Singular Value Decomposition and Its Simple Application

关于矩阵分解有多种形式,而在实际应用中奇异值分解尤为重要,借助由S(α)=Aα式所确定的S:Rn→Rm线性映射,给出了矩阵奇异值分解定理更具几何直观的推导过程,并用实例对其进行了辅证.

There are many forms of matrix decomposition,among which singular value decomposition is especially important in real application. Therefore,by using S： Rn→Rmlinear maps determined by the type of S（ α） = Aα,the paper puts forward a more intuitively geometrical derivation process for matrix singular value decomposition theorem and an example is used to provide supporting information.