What does orthogonality mean?
Orthogonality names the relationship between things that meet at a right angle, most commonly lines or directions in geometry. In linear algebra, it has a precise algebraic meaning: two vectors are orthogonal when their dot product is zero. A collection of objects can be described as mutually orthogonal when each one is perpendicular to all the others. The term is especially important in coordinate geometry, where perpendicular axes make position and movement easier to describe, and in matrix theory and signal processing, where orthogonal directions help separate or simplify complex relationships. Although “orthogonality” is closely related to the adjective “orthogonal,” it is used when the mathematical relationship itself, rather than an individual line, vector, or arrangement, is being discussed. In ordinary English, the word is technical and generally appears in academic, scientific, or mathematical contexts.
nounOrthogonality is the state or condition of being orthogonal, especially of lines or vectors that meet at a right angle. In mathematics, it also describes vectors whose dot product is zero, or a set of directions that are mutually perpendicular.
- The condition of two lines or directions being perpendicular, or at right angles to one another.
- In linear algebra, the property of vectors whose dot product is zero, indicating that they are perpendicular in the relevant vector space.
- The condition of a collection of lines, vectors, or other mathematical objects being mutually perpendicular.
"The orthogonality of the coordinate axes allows each vector to be described by independent horizontal and vertical components."
"The orthogonality of the two axes makes the coordinate system especially useful for describing position."
"The algorithm assumes orthogonality between the selected features, which helps reduce redundant information."
The plural is used when referring to separate orthogonal relationships, especially between different pairs or sets of mathematical objects.
"The orthogonality of the basis vectors makes the change of coordinates straightforward."
In linear algebra, orthogonality turns difficult relationships between vectors into clean, independent directions.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does orthogonality come from?
The word comes from the Greek adjective orthogōnios, formed from orthos, “straight” or “correct,” and gōnia, “angle,” and was used for “having a right angle.” It entered English through the mathematical adjective “orthogonal,” with the abstract noun “orthogonality” developing later from that established form. The same Greek roots also underlie related words such as “orthogonous,” while “orthogonal” remains the standard modern English derivative.
Related word forms
How orthogonality is actually used
Orthogonality is chiefly a technical term used in geometry, linear algebra, and related mathematical fields. It is formal and specialized rather than part of everyday vocabulary.
Easily confused with orthogonality
Orthogonality concerns right angles and mathematical perpendicularity, whereas orthography concerns the conventional spelling and writing system of a language.