# Orthogonal

[awr-thog-uh-nl] /ɔrˈθɒg ə nl/

**adjective**

1.

Mathematics.

2.

Crystallography. referable to a rectangular set of axes.

/ɔːˈθɒɡənəl/

**adjective**

1.

relating to, consisting of, or involving right angles; perpendicular

2.

(maths)

**adj.**

1570s, from French orthogonal, from orthogone, from Late Latin orthogonius, from Greek orthogonios “right-angled,” from ortho- “straight” (see ortho-) + gonia “angle,” related to gony “knee” (see knee (n.)). Related: Orthogonally.

orthogonal

(ôr-thŏg’ə-nəl)

geometry

At 90 degrees (right angles).

N mutually orthogonal vectors span an N-dimensional vector space, meaning that, any vector in the space can be expressed as a linear combination of the vectors. This is true of any set of N linearly independent vectors.

The term is used loosely to mean mutually independent or well separated. It is used to describe sets of primitives or capabilities that, like linearly independent vectors in geometry, span the entire “capability space” and are in some sense non-overlapping or mutually independent. For example, in logic, the set of operators “not” and “or” is described as orthogonal, but the set “nand”, “or”, and “not” is not (because any one of these can be expressed in terms of the others).

Also used loosely to mean “irrelevant to”, e.g. “This may be orthogonal to the discussion, but …”, similar to “going off at a tangent”.

See also orthogonal instruction set.

[Jargon File]

(2002-12-02)

Tagged: o

Read Also:

- Orthogonal instruction set
architecture An instruction set where all (or most) instructions have the same format and all registers and addressing modes can be used interchangeably – the choices of op code, register, and addressing mode are mutually independent (loosely speaking, the choices are “orthogonal”). This contrasts with some early Intel microprocessors where only certain registers could be […]

- Orthogonalise
[awr-thog-uh-nl-ahyz] /ɔrˈθɒg ə nlˌaɪz/ verb (used with object), orthogonalized, orthogonalizing. Mathematics. 1. to make (vectors, functions, etc.) .

- Orthogonalize
[awr-thog-uh-nl-ahyz] /ɔrˈθɒg ə nlˌaɪz/ verb (used with object), orthogonalized, orthogonalizing. Mathematics. 1. to make (vectors, functions, etc.) .

- Orthogonally
[awr-thog-uh-nl] /ɔrˈθɒg ə nl/ adjective 1. Mathematics. 2. Crystallography. referable to a rectangular set of axes. /ɔːˈθɒɡənəl/ adjective 1. relating to, consisting of, or involving right angles; perpendicular 2. (maths) adj. 1570s, from French orthogonal, from orthogone, from Late Latin orthogonius, from Greek orthogonios “right-angled,” from ortho- “straight” (see ortho-) + gonia “angle,” related to […]