【摘要】 教学过程中，学生往往对多个线性子空间的和构成直和的等价条件理解错误或者理解不够深刻.首先，分析多个子空间直和的判定条件中学生的常见错误；其次，通过定理证明明确判定条件；最后，结合易错点给出相关的推论以强化理解.更多还原

【Abstract】 In the teaching process, students often misunderstand or fail to grasp the equivalent conditions for determining when the sum of multiple linear subspaces forms a direct sum. This paper first analyzes the common errors students make regarding the conditions for determining the direct sum of multiple subspaces and then proves relevant judging theorems. Finally, instructive corollaries focusing on error-prone conditions are provided to deepen students’ understanding.更多还原