TITLE: What is the meaning of superscript $\perp$ for a vector space
QUESTION [8 upvotes]: If $A$ is a matrix, then the nullspace of $A$, i.e. $null(A)$, is a vector subspace. Then, what is the meaning of superscript inverted $T$, for example $$null(A)^\perp$$
on a vector subspace?

REPLY [9 votes]: It $A^\perp$ means orthogonal complement of $A$, meaning the subspace that consists of all vectors which when dotted with any vector from $A$ produce $0$, that is
$$A^\perp = \left \{ \right. \vec{x} \ | \ \vec{x} \cdot \vec{y}=0, \ \ \forall \vec{y} \in A \left.  \right \}$$
More at http://en.wikipedia.org/wiki/Orthogonal_complement.