Orthogonality

Part of speech: noun

Pronunciation: /ɔːˌθɒɡ.əˈnæl.ɪ.ti/

Definitions

1. The quality of two lines or vectors being at right angles to each other in a geometric or algebraic space
2. A condition where elements such as functions or vectors are mutually perpendicular or independent in mathematical contexts
3. The state of maintaining perpendicularity between components in areas like geometry or linear algebra

Etymology: "Orthogonality" is simply "orthogonal" with the suffix "-ity" added, and the suffix does most of the work of turning a shape into a concept. "Orthogonal" itself comes from Greek roots meaning "right-angled" (orthos, "straight" or "upright," plus gonia, "angle"), so the core idea is a pair of lines meeting at a right angle. The "-ity" ending comes from Latin "-itas," which passed into English through Old French and Middle English, and it turns an adjective into a noun naming a state or quality. The result is a noun for the condition of being perpendicular, extended beyond simple lines to abstract spaces. In linear algebra, two vectors are orthogonal when their dot product is zero, and orthogonality names the property that holds across whole sets of such vectors. The word therefore moved from describing a corner of a room to describing a relationship between mathematical objects that cannot be drawn.

Synonyms: perpendicularity, independence, unrelatedness, non-correlation, right angle

Antonyms: dependency, correlation, relationship, association, connectedness