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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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    It's also the annihilator, which sometimes reduces to orthogonal complement.2013-08-27

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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.