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{{was wotd|2006|April|25}}

English

Etymology

Mediaeval orthogonalis, from Latin orthogonius "right-angled".

Pronunciation

  • IPA: /ɔ:'θɒgənəl/
  • An audio transcript can be found at en-us-orthogonal.ogg


Adjective

orthogonal (non-comparable)

  1. pertaining to right angles; perpendicular (to)
  2. : A chord and the radius that bisects it are orthogonal.
  3. mathematical use
    1. Of two functions, linearly independent; having a zero inner product.
    2. : The normal vector and tangent vector at a given point are orthogonal.
    3. Of a square matrix that is the inverse of its transpose
    4. Of a linear transformation that preserves angles
  4. statistically independent, with reference to variates
  5. Able to be treated separately.
  6. : The content of the message should be orthogonal to the means of its delivery.


Derived terms


Related terms


Translations

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French

Etymology

Mediaeval Latin orthogonalis, from late Latin orthogonius "right-angled".

Pronunciation

IPA: /ɔʀtɔgɔnal/

Adjective

  1. orthogonal#English|orthogonal


Category:French adjectives Category:Geometry Category:Mathematics

de:orthogonal el:orthogonal fr:orthogonal io:orthogonal hu:orthogonal pl:orthogonal ru:orthogonal sv:orthogonal ta:orthogonal vi:orthogonal zh:orthogonal

GNU Project's publication of CIDE, the Collaborative International Dictionary of English Orthogonal \Or*thog"o*nal\, a. [Cf. F. orthogonal.]
Right-angled; rectangular; as, an orthogonal intersection of
one curve with another.
[1913 Webster]

Orthogonal projection. See under Orthographic.
[1913 Webster]
WordNet orthogonal
adj 1: not pertinent to the matter under consideration; "an issue
extraneous to the debate"; "the price was immaterial";
"mentioned several impertinent facts before finally
coming to the point" [syn: extraneous, immaterial,
impertinent]
2: statistically unrelated
3: having a set of mutually perpendicular axes; meeting at
right angles; "wind and sea may displace the ship's center
of gravity along three orthogonal axes"; "a rectangular
Cartesian coordinate system" [syn: rectangular]
Moby Dictionary
cube-shaped , cubed , cubic , cubiform , cuboid , diced , foursquare ,
normal , oblong , orthodiagonal , orthometric , perpendicular , plumb ,
plunging , precipitous , quadrangular , quadrate , quadriform ,
quadrilateral , rectangular , rhombic , rhomboid , right-angle ,
right-angled , right-angular , sheer , square , steep , straight-up ,
straight-up-and-down , tetragonal , tetrahedral , trapezohedral ,
trapezoid , up-and-down


Jargon orthogonal adj. [from mathematics] Mutually independent; well
separated; sometimes, irrelevant to. Used in a generalization of its
mathematical meaning to describe sets of primitives or capabilities
that, like a vector basis in geometry, span the entire `capability
space' of the system and are in some sense non-overlapping or mutually
independent. For example, in architectures such as the PDP-11 or VAX
where all or nearly all registers can be used interchangeably in any
role with respect to any instruction, the register set is said to be
orthogonal. Or, in logic, the set of operators `not' and `or' is
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 in comments
on human discourse: "This may be orthogonal to the discussion, but...."


FOLDOC orthogonal

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)


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