有限维线性空间中线性变换值域与核的关系

The Relationship between Range and Kernel of Linear Transformations of Finite Dimensional Linear Space

本文给出了线性变换的值域与核的内在关系,讨论了线性空间分解为线性变换值域与核的直和的充要条件以及线性变换值域与核的包含关系。

This paper presents the intrinsic relationship of range and kernel of linear transformations,discusses the necessary and sufficient conditions for the direct sum decomposition of range and kernel of linear transformation in linear space and the inclusion relation of range and kernel of linear transformation.