Posted by haifeng on 2015-07-27 11:09:04 last update 2015-07-27 11:09:48 | Answers (1) | 收藏
设 $U,V$ 为向量空间 $W$ 的子向量空间, 则 $U,V$ 横截相交当且仅当 $U+V=W$, 此时
\[ \dim(U\cap V)=\dim U+\dim V-\dim W. \]
或改写为
\[ \text{codim} U\cap V=\text{codim} U+\text{codim} V. \]
这里 $\text{codim}(U)=\dim W-\dim U$.
