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orthogonal complement

W^\perp — every vector orthogonal to all of a subspace W at once.

For a subspace W, the orthogonal complement W^\perp is the set of every vector orthogonal to every vector in W. It is itself a subspace, and every vector \mathbf y splits uniquely as \mathbf y=\hat{\mathbf y}+\mathbf z with \hat{\mathbf y}\in W and \mathbf z\in W^\perp.

See also

orthogonal set orthogonal decomposition theorem
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