orthogonal

From Middle French orthogonal, in turn from Medieval Latin orthogōnālis and Latin orthogōnius (“right-angled”), ultimately from Ancient Greek ὀρθογώνιος (orthogṓnios, “rectangular”).^[1] By surface analysis, ortho- +‎ -gon +‎ -al.

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

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• Audio (UK):

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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.

orthogonal (plural orthogonals)

1. An orthogonal line.

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

• uncorrelated

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

• IPA^(key): /ɔʁ.to.ɡo.nal/

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

1. orthogonal

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

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

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• Rhymes: -aːl

orthogonal (strong nominative masculine singular orthogonaler, not comparable)

1. orthogonal

   Synonym: senkrecht

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