orthogonal

adj, noun — 10 senses

orthogonal

adj

UK /ɔːˈθɒɡ.ə.nəl/ · US /ɔɹˈθɑ.ɡə.nəl/

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.

9 senses
  1. 1Of two objects, at right angles; perpendicular to each other.
  2. 2Of a pair of vectors: having a zero inner product; perpendicular.
  3. 3Of a square matrix: such that its transpose is equal to…
  4. 4Of a linear transformation: preserving its angles.
  5. 5Of grid graphs, board games and polyominoes: vertical or…
  6. 6Of a pair of elements in an ortholattice: each less than…
  7. 7Statistically independent, with reference to variates.
  8. 8Of two or more aspects of a problem, able to be treated…
  9. 9Of two or more problems or subjects, independent of or…
1

Geometry, Mathematics, Sciences Of two objects, at right angles; perpendicular to each other.

  • A chord and the radius that bisects it are orthogonal.
2

Mathematics, Sciences Of a pair of vectors: having a zero inner product; perpendicular.

  • The normal vector and tangent vector at a given point are orthogonal.
3

Mathematics, Sciences Of a square matrix: such that its transpose is equal to its inverse.

4

Mathematics, Sciences Of a linear transformation: preserving its angles.

5

Mathematics, Sciences Of grid graphs, board games and polyominoes: vertical or horizontal but not diagonal.

6

Mathematics, Sciences Of a pair of elements in an ortholattice: each less than or equal to the orthocomplement of the other.

7

Mathematics, Sciences, Statistics Statistically independent, with reference to variates.

8

Computing, Engineering, Mathematics, Natural sciences, Physical sciences, Sciences, Software 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.
  • 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.1999, Andrew Hunt, David Thomas, The Pragmatic Programmer: From Journeyman to Master, Addison-Wesley Professional, →ISBN, page 36:
9

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

  • 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.2014 March 22, Rick Weber, “Polystate: Book 2”, in Notes on Liberty:
Antonyms
unorthogonal
Derived terms
orthogonal base, orthogonal complement, orthogonal function, orthogonal group, orthogonality, orthogonalize, orthogonally, orthogonal matrix, orthogonals, orthogonal transform
Related terms
orthogonalization, orthonormal, semiorthogonal
Hyponyms
bioorthogonal

orthogonal

noun

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.

1

An orthogonal line.

  • All of the orthogonals in this painting display an understanding of linear perspective.
Related terms
uncorrelated

Entry derived from the Wiktionary, under licence CC BY-SA 4.0 — list of authors.