orthogonal

English

WOTD – 25 April 2006

Etymology

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

Pronunciation

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

• Audio (US)

  (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

Related terms

Terms related to orthogonal

• 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

• 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
• Norwegian:

  Bokmål: ortogonal

  Nynorsk: ortogonal

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

statistically independent

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

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

able to be treated separately

• French: indépendant (fr)

• Irish: ortagánach, ingearach
• Spanish: independiente (es)

See also

• uncorrelated

---

French

Etymology

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

Pronunciation

• IPA^(key): /ɔʁtɔɡɔnal/

Adjective

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

1. orthogonal

Further reading

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

---

German

Etymology

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

Pronunciation

• Audio

  (file)

• Rhymes: -aːl

Adjective

orthogonal (not comparable)

1. orthogonal

Declension

Declension of orthogonal

number & gender		singular			plural
		masculine	feminine	neuter	all genders
predicative		er ist orthogonal	sie ist orthogonal	es ist orthogonal	sie sind orthogonal
strong declension (without article)	nominative	orthogonaler	orthogonale	orthogonales	orthogonale
	genitive	orthogonalen	orthogonaler	orthogonalen	orthogonaler
	dative	orthogonalem	orthogonaler	orthogonalem	orthogonalen
	accusative	orthogonalen	orthogonale	orthogonales	orthogonale
weak declension (with definite article)	nominative	der orthogonale	die orthogonale	das orthogonale	die orthogonalen
	genitive	des orthogonalen	der orthogonalen	des orthogonalen	der orthogonalen
	dative	dem orthogonalen	der orthogonalen	dem orthogonalen	den orthogonalen
	accusative	den orthogonalen	die orthogonale	das orthogonale	die orthogonalen
mixed declension (with indefinite article)	nominative	ein orthogonaler	eine orthogonale	ein orthogonales	(keine) orthogonalen
	genitive	eines orthogonalen	einer orthogonalen	eines orthogonalen	(keiner) orthogonalen
	dative	einem orthogonalen	einer orthogonalen	einem orthogonalen	(keinen) orthogonalen
	accusative	einen orthogonalen	eine orthogonale	ein orthogonales	(keine) orthogonalen

Synonyms

• senkrecht