矩阵奇异值分解定理的直观证明

摘要

Singular value decomposition theorem is a fundamental theorem of matrix theory.Usually,the proof of theorem in traditional textbooks lacks geometric intuition.Gave alternative proof with geometric intuition of real matrix singular value decomposition theorem by using orthogonal projection and basic limit of trigonometric.%矩阵的奇异值分解定理是矩阵论的一个基本定理。传统教材中给出的证明方法往往缺乏几何直观。为此，借助正交投影和一个基本三角函数的极限，给出实矩阵奇异值分解定理证明方法的一个更具几何直观的备选方案。