# What is the meaning of superscript $\perp$ for a vector space

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?

• Usually it's the orthogonal complement. – Ryan Budney May 11 '11 at 0:41
• It's called the orthogonal complement. – t.b. May 11 '11 at 0:41
• It's also the annihilator, which sometimes reduces to orthogonal complement. – scineram Aug 27 '13 at 0:06

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
$$A^\perp = \left \{ \right. \vec{x} \ | \ \vec{x} \cdot \vec{y}=0, \ \ \forall \vec{y} \in A \left. \right \}$$