orthogonal

English

WOTD – 25 April 2006

Etymology

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

Pronunciation

• IPA^(key): /ɔːˈθɒɡənəl/
• IPA^(key): /ɔɹˈθɑɡənəl/

• Audio (US)

  (file)

• Audio (AU)

  (file)

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
• orthogonals

Related terms

• biorthogonal
• orthogonal base
• orthogonalization
• orthogonal matrix
• orthogonal transform
• orthonormal
• semiorthogonal

 

Translations

of right angles

• Catalan: ortogonal
• Danish: ortogonal, vinkelret (da)
• Dutch: orthogonaal (nl), loodrecht (nl)
• Finnish: ortogonaalinen (fi), suorakulmainen (fi)
• French: orthogonal (fr)
• German: rechtwinklig (de)
• Greek: ορθογώνιος (el) (orthogónios)
• Hungarian: ortogonális (hu)
• Irish: ortagánach, ingearach, dronuilleach
• (deprecated template usage) {{trans-mid}}
• Italian: ortogonale (it)
• Norwegian:

  Bokmål: ortogonal

  Nynorsk: ortogonal

• Portuguese: ortogonal (pt), perpendicular (pt)
• Russian: прямоуго́льный (ru) (prjamougólʹnyj), ортогона́льный (ru) (ortogonálʹnyj)
• Spanish: ortogonal (es)
• Swedish: ortogonal (sv), vinkelrät (sv), rätvinklig (sv)

mathematical term

• Catalan: ortogonal
• Dutch: orthogonaal (nl)
• French: orthogonal (fr)
• Georgian: მართკუთხა (martḳutxa)
• German: senkrecht (de), orthogonal (de)
• Hungarian: ortogonális (hu)
• Irish: ortagánach, ingearach
• (deprecated template usage) {{trans-mid}}
• Norwegian:

  Bokmål: ortogonal

  Nynorsk: ortogonal

• Russian: ортогона́льный (ru) (ortogonálʹnyj)
• Spanish: ortogonal (es)
• Swedish: ortogonal (sv)

statistically independent

• French: orthogonal (fr)
• Irish: ortagánach, ingearach
• (deprecated template usage) {{trans-mid}}
• Russian: ортогона́льный (ru) (ortogonálʹnyj)
• Swedish: ortogonal (sv)

able to be treated separately

• French: indépendant (fr)
• Irish: ortagánach, ingearach
• (deprecated template usage) {{trans-mid}}
• Spanish: independiente (es)

Noun

orthogonal (plural orthogonals)

1. An orthogonal line

See also

• uncorrelated

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French

Etymology

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

Pronunciation

• IPA^(key): /ɔʁ.to.ɡo.nal/

Adjective

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

1. orthogonal

Further reading

• “orthogonal”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012.

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German

Etymology

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

Pronunciation

• Audio

  (file)

• Rhymes: -aːl

Adjective

orthogonal (not comparable)

1. orthogonal

Synonyms

• senkrecht