# orthogonal
## English
### 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: /ɔːˈθɒɡ.ə.nəl/
* (US) IPA: /ɔɹˈθɑɡ.ə.nəl/
** Audio (US):(file)
* Audio (UK):(file)

### Adjective

orthogonal (not comparable)
* (geometry) Of two objects, at right angles; perpendicular to each other.
    A chord and the radius that bisects it are orthogonal.
* (mathematics)
** Of a pair of vectors: having a zero inner product; perpendicular.
    The normal vector and tangent vector at a given point are orthogonal.
** Of a square matrix: such that its transpose is equal to its inverse.
** Of a linear transformation: preserving its angles.
** Of grid graphs, board games and polyominoes: vertical or horizontal but not diagonal.
** Of a pair of elements in an ortholattice: each less than or equal to the orthocomplement of the other.
* (statistics) Statistically independent, with reference to variates.
* (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.
* 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: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
### Noun

orthogonal (plural orthogonals)
* An orthogonal line.
    All of the orthogonals in this painting display an understanding of linear perspective.

### See also

* uncorrelated

### References

* ↑ “orthogonal, adj.”, in OED Online ⁠, Oxford: Oxford University Press, launched 2000.

## French
### Etymology

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

### Pronunciation

* IPA: /ɔʁ.to.ɡo.nal/
* Audio:(file)

### Adjective

orthogonal (feminine orthogonale, masculine plural orthogonaux, feminine plural orthogonales)
* 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)
* orthogonal
    Synonym: senkrecht

#### Declension
### Further reading

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