# unitary

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## English

### Pronunciation

• (UK) IPA(key): /juːnɪt(ə)ɹi/
•  Audio (Southern England) (file)

### Adjective

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

• (that contains an identity element): unital

#### Antonyms

• (that concentrates power in a single body): confederal

### 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.
• 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?