orthogonal

English

WOTD – 25 April 2006

Wikipedia

Etymology

From French orthogonal, from Medieval Latin orthogonalis, from Latin orthogonius (“right-angled”).

Pronunciation

• IPA^(key): /ɔːˈθɒɡənəl/

• Audio (US)

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Adjective

orthogonal (not comparable)

1. (geometry) Of two objects, at right angles; perpendicular to each other.

   A chord and the radius that bisects it are orthogonal.

2. (mathematics)
   1. Of a pair of vectors: having a zero inner product; perpendicular.

      The normal vector and tangent vector at a given point are orthogonal.

   2. Of a square matrix: such that its transpose is equal to its inverse.
   3. Of a linear transformation: preserving its angles.
   4. Of grid graphs, board games and polyominoes: vertical or horizontal but not diagonal.
3. (statistics) Statistically independent, with reference to variates.
4. (software engineering) Of two or more aspects of a problem, able to be treated separately.

   The content of the message should be orthogonal to the means of its delivery.

5. Of two or more problems or subjects, independent of or irrelevant to each other.

Derived terms

• orthogonality

Related terms

• orthogonalization
• orthogonal base
• orthogonal matrix
• orthogonal transform
• orthonormal

See also

• uncorrelated

Translations

of right angles

• Catalan: ortogonal
• Danish: ortogonal, vinkelret
• Dutch: orthogonaal (nl), loodrecht (nl)
• Finnish: ortogonaalinen, suorakulmainen (fi)
• French: orthogonal (fr)
• German: rechtwinklig (de)

• Greek: ορθογώνιος (el) (orthogónios)
• Hungarian: ortogonális (hu)
• Irish: ortagánach, ingearach
• Portuguese: ortogonal, perpendicular (pt)
• Russian: прямоуго́льный (ru) (prjamougólʹnyj), ортогона́льный (ru) (ortogonálʹnyj)
• Swedish: ortogonal, vinkelrät (sv), rätvinklig (sv)

mathematical term

• Catalan: ortogonal
• Dutch: orthogonaal (nl)
• French: orthogonal (fr)
• German: orthogonal (de)

• Hungarian: ortogonális (hu)
• Irish: ortagánach, ingearach
• Russian: ортогона́льный (ru) (ortogonálʹnyj)
• Swedish: ortogonal

statistically independent

• French: orthogonal (fr)
• Irish: ortagánach, ingearach

• Russian: ортогона́льный (ru) (ortogonálʹnyj)
• Swedish: ortogonal

able to be treated separately

• French: indépendant (fr)

• Irish: ortagánach, ingearach

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French

Etymology

From Ancient Greek ορθός (orthós, “correct, straight, right”) and γωνία (gōnía, “angle”).

Pronunciation

• IPA^(key): /ɔʁtɔɡɔnal/

Adjective

orthogonal m (feminine singular orthogonale, masculine plural orthogonaux, feminine plural orthogonales)

1. orthogonal

External links

• “orthogonal” in le Trésor de la langue française informatisé (The Digitized Treasury of the French Language).