orthogonal

English

WOTD – 25 April 2006

Etymology

From Middle French orthogonal, in turn from Medieval Latin orthogōnālis and Latin orthogōnius (“right-angled”), ultimately from Ancient Greek ὀρθογώνιος (orthogṓnios, “rectangular”). By surface analysis, ortho- +‎ -gon +‎ -al.

Pronunciation

• (UK) IPA^(key): /ɔːˈθɒɡ.ə.nəl/
• (US) IPA^(key): /ɔɹˈθɑɡ.ə.nəl/

  • Audio (US):

    (file)

• Audio (UK):

  (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.
   5. Of a pair of elements in an ortholattice: each less than or equal to the orthocomplement of the other.
3. (statistics) Statistically independent, with reference to variates.
4. (software engineering) Of two or more aspects of a problem, able to be treated separately; of a design, exhibiting consistency and composability.

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

   • 1999, Andrew Hunt, David Thomas, The Pragmatic Programmer: From Journeyman to Master, Addison-Wesley Professional, →ISBN, page 36:

     An orthogonal approach also promotes reuse. If components have specific, well-defined responsibilities, they can be combined with new components in ways that were not envisioned by their original implementors.

5. Of two or more problems or subjects, independent of or irrelevant to each other.
   • 2014 March 22, Rick Weber, “Polystate: Book 2”, in Notes on Liberty‎^[1]:

     Even in a geostate, some people are willing to fight and die for their views, but the institutional change to a polystate seems somewhat orthogonal to such issues.

Derived terms

• orthogonal complement
• orthogonal function
• orthogonal group
• orthogonality
• orthogonals

Related terms

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

Translations

of right angles

• Bulgarian: правоъгълен (pravoǎgǎlen)
• Catalan: ortogonal
• Czech: pravoúhlý (cs)
• Danish: ortogonal, vinkelret (da)
• Dutch: orthogonaal (nl), loodrecht (nl)
• Finnish: ortogonaalinen (fi), suorakulmainen (fi)
• French: orthogonal (fr)
• German: rechtwinklig (de)
• Greek: ορθογώνιος (el) (orthogónios)
• Hindi: लांबिक (lāmbik), लंब कोणीय (lamb koṇīya)
• 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
• Chinese:

  Mandarin: 正交的 (zh) (zhèngjiāo de)

• Czech: kolmý (cs)
• Dutch: orthogonaal (nl)
• Finnish: ortogonaalinen (fi)
• 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

• Finnish: tilastollisesti riippumaton
• French: orthogonal (fr)
• Irish: ortagánach, ingearach
• Russian: ортогона́льный (ru) (ortogonálʹnyj)
• Swedish: ortogonal (sv)

software: able to be treated separately

• Finnish: riippumaton (fi)
• French: indépendant (fr)
• Irish: ortagánach, ingearach
• Spanish: independiente (es)

Noun

orthogonal (plural orthogonals)

1. An orthogonal line.

   All of the orthogonals in this painting display an understanding of linear perspective.

See also

• uncorrelated

French

Etymology

Borrowed from Medieval Latin orthogōnālis, from Latin orthogōnius (“right-angled”).

Pronunciation

• IPA^(key): /ɔʁ.to.ɡo.nal/

• Audio:

  (file)

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.

German

Etymology

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

Pronunciation

• Audio:

  (file)

• Rhymes: -aːl

Adjective

orthogonal (strong nominative masculine singular orthogonaler, not comparable)

1. orthogonal

   Synonym: senkrecht

Declension

Positive forms of orthogonal (uncomparable)

number & gender		singular			plural
		masculine	feminine	neuter
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

Further reading

• “orthogonal” in Digitales Wörterbuch der deutschen Sprache
• “orthogonal” in Uni Leipzig: Wortschatz-Lexikon