orthogonal

English dictionary entry

Meanings

adj

Of two objects, at right angles; perpendicular to each other.
Of a pair of vectors: having a zero inner product; perpendicular.
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.
Statistically independent, with reference to variates.
Of two or more aspects of a problem, able to be treated separately; of a design, exhibiting consistency and composability.
Of two or more problems or subjects, independent of or irrelevant to each other.

noun

An orthogonal line.

Pronunciation

/ɔːˈθɒɡ.ə.nəl/ /ɔɹˈθɑ.ɡə.nəl/ en-us-orthogonal.ogg /ɔɹˈθɒɡ.ə.nəl/ /oːˈθɔɡ.ə.nəl/ en-au-orthogonal.ogg /oːˈθɒɡ.ə.nəl/ [oːˈθɔ̟ɡ.ə.nəl]

Word forms

orthogonal orthogonals

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.

Related words

biorthogonal orthogonal base orthogonalization orthogonal matrix orthogonal transform orthonormal semiorthogonal uncorrelated

Derived words

bioorthogonal nonorthogonal orthogonal complement orthogonal function orthogonal group orthogonality orthogonalize orthogonally orthogonals unorthogonal

Translations

Catalan: ortogonal Chinese Mandarin: 正交的 Czech: kolmý Dutch: orthogonaal Finnish: ortogonaalinen French: orthogonal Georgian: მართკუთხა German: senkrecht German: orthogonal Hungarian: ortogonális Irish: ortagánach Irish: ingearach Kazakh: ортогоналды Kazakh: ортогоналдық Norwegian Bokmål: ortogonal Norwegian Nynorsk: ortogonal Polish: prostopadły Polish: ortogonalny Russian: ортогона́льный Spanish: ortogonal Swedish: ortogonal

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