unitary

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Pronunciation

• (British) IPA: /juːnɪt(ə)ɹi/

Adjective

1. Having the quality of oneness.
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, analysis, of a matrix or operator) Whose inverse is equal to its adjoint.
   • 1997, M. E. Alferieff (translator), P. K. Suetin, Alexandra I. Kostrikin, Yuri I. Manin, 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, 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 U_k. 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

• (that contains an identity element) unital

Antonyms

• (that concentrates power in a single body) federalist

Related terms

• unitariness
• unitarily
• unitarity

Translations

• French: unitaire
• Portuguese: unitário
• Russian: едини́чный
• Spanish: unitario

Translations

• French: unitaire
• Italian: unitario
• Portuguese: unitário
• Russian: еди́ный
• Spanish: unitario

Translations

• Portuguese: unitário
• Russian: унита́рный
• Spanish: unitario

Noun

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.

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