垂直的两个平面不是正交子空间

hbghlyj

linear-algebra-fall-2011
Subspace $S$ is orthogonal to subspace $T$ means: every vector in $S$ is orthogonal to every vector in $T$. The blackboard is not orthogonal to the floor; two vectors in the line where the blackboard meets the floor aren’t orthogonal to each other.

在$\Bbb R^3$中, 垂直的两个平面作为线性子空间不是正交的
直线与平面垂直, 它们为正交子空间. 而且它们的和为全空间, 所以是正交补.