线性变换的像与核对空间的直和分解

摘要

The image and kernel of linear transformation find significant application in the direct sum decomposition for finite dimension of linear space and the diagonalization of matrices.This paper studies the conditions for the idempotent transformation and the idempotent rank transformation direct sum decomposi-tion for finite dimension of linear space.And the direct sum decomposition is finally extended to any linear transformation.It provides abundant theory tools for researches of these questions.%线性变换的像与核在空间的直和分解及矩阵对角化问题中都有重要应用。文章分别给出了幂等变换及幂等秩线性变换对空间直和分解所需满足的条件，并最终将该直和分解推广到一般的线性变换上来，为上述问题的研究提供了更为丰富的理论工具。