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unitary

From Wiktionary, the free dictionary

English

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Etymology

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Etymology tree
English unit
Proto-Indo-European *-yósder.
Proto-Italic *-āzios
Latin -āriusder.
Middle English -arie
English -ary
English unitary

    From unit + -ary.

    Pronunciation

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    Adjective

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    unitary

    1. Having the quality of oneness.
      • 2004, Andrew Radford, Minimalist Syntax: Exploring the Structure of English, Cambridge, UK: Cambridge University Press, page 221:
        If yes–no questions are CPs containing a null yes–no question operator (a null counterpart of whether) in spec-CP, we can arrive at a unitary characterisation of questions as CPs with an interrogative specifier.
    2. (government, of a system of government or administration) That concentrates power in a single body, rather than sharing it with more local bodies.
      a unitary authority
      a unitary state
    3. (mathematics, of an algebra) That contains an identity element.
    4. (mathematics, linear algebra, mathematical analysis, of a matrix or operator) Whose inverse is equal to its adjoint.
      • 1997, P. K. Suetin, Alexandra I. Kostrikin, Yuri I. Manin, translated by M. E. Alferieff, Linear Algebra and Geometry, page 137:
        The eigenvectors of an orthogonal or unitary operator, corresponding to different eigenvalues, are orthogonal.
      • 2002, M. Klajman, J. A. Chambers, “A Novel Approximate Joint Diagonalization Algorithm”, in J. G. McWhirter, I. K. Proudler, editors, Mathematics in Signal Processing V, page 71:
        In essence we are looking for some way to average the individual unitary matrices Uk. But a linear combination of unitary matrices does not remain unitary.
      • 2008, Mikio Nakahara, Tetsuo Ohmi, Quantum Computing: From Linear Algebra to Physical Realizations, page 84:
        We then repeat the same procedure to the (d − 1) × (d − 1) block unitary matrix using (d − 2) two-level unitary matrices.

    Synonyms

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    • (that contains an identity element): unital

    Antonyms

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    • (antonym(s) of “that concentrates power in a single body”): confederal

    Derived terms

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    Translations

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    government: that concentrates power into a single body

    See also

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    Noun

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    unitary (plural unitaries)

    1. (UK) A unitary council.
      • 2005, John Greenwood, Robert Pyper, David Wilson, New Public Administration in Britain:
        Outside the metropolitan areas most councils (English and Welsh counties, London boroughs, Scottish and Welsh unitaries, and Northern Ireland districts) are now elected en bloc every four years.
    2. (mathematics) A unitary matrix or operator.
      • 1980, Michael Reed, Barry Simon, Methods of Modern Mathematical Physics, Volume 1: Functional Analysis, Revised and Expanded Edition page 243,
        Since ergodicity and mixing are expressible in terms of the induced Koopman unitaries they are not additional invariants.
      • 2001, Huaxin Lin, An Introduction to the Classification of Amenable C*-Algebras‎[1], page 170:
        Can unitaries in a unital C*-algebra with real rank zero be approximated by unitaries with finite spectrum?

    Derived terms

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