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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?

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

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