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unitary

From Wiktionary, the free dictionary

English

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Etymology

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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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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?
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