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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5$\begingroup$ Usually it's the orthogonal complement. $\endgroup$– Ryan BudneyCommented May 11, 2011 at 0:41
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6$\begingroup$ It's called the orthogonal complement. $\endgroup$– t.b.Commented May 11, 2011 at 0:41
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1$\begingroup$ It's also the annihilator, which sometimes reduces to orthogonal complement. $\endgroup$– scineramCommented Aug 27, 2013 at 0:06
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1 Answer
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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
$$A^\perp = \left \{ \right. \vec{x} \ | \ \vec{x} \cdot \vec{y}=0, \ \ \forall \vec{y} \in A \left. \right \}$$
answered May 11, 2011 at 0:45