Overview of Orthogonal Complements

A detailed tutorial on orthogonal complements. Step by step tutorial including several examples of orthogonal complements for reference.

The orthogonal complement of a subspace of an inner product space is the set of all vectors in the inner product space that are orthogonal to every vector in the subspace. This can be expressed mathematically in the formula , where W is the subspace and V is the inner product space. The orthogonal complement is sometimes also called the perpendicular complement, shortened to the informal form perp.

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