Orthogonality

In mathematics, orthogonal is synonymous with perpendicular when used as a simple adjective that is not part of any longer phrase with a standard definition. It means at right angles. It comes from the Greek "ortho", meaning "right", and "gonia", meaning "angle". Two streets that cross each other at a right angle are orthogonal to each other. Two vectors in an inner product space are orthogonal if their inner product is zero. If the vectors are x and y this is written x perp y. The word normal is sometimes also used for this concept by mathematicians, although that word is rather overburdened.

Related Topics:
Mathematics - Perpendicular - Right angle - Greek - Inner product space

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Two subspaces are called orthogonal if each vector in one is orthogonal to each vector in the other. Note however that this does not correspond with the geometric concept of perpendicular planes. The largest subspace that is orthogonal to a given subspace is its orthogonal complement.

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