# What is the meaning of superscript ⊥ for a vector space

This should be an easy question, if A is a matrix, then the nullspace of A is a vector (sub)space. Then, what is the meaning of superscript inverted T on a vector (sub)space? e.g. $(\mathrm {nullspace } A)^⊥$.

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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

## 1 Answer

It $A^⊥$ 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, $A^⊥$= $\left \{ \right. \vec{x} \ | \ \vec{x} \cdot \vec{y}=0, \ \ \forall \vec{y} \in A \left. \right \}$. More at http://en.wikipedia.org/wiki/Orthogonal_complement.

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