unitary

unitary

1. Having the quality of oneness.
   • 2004, Andrew Radford, Minimalist Syntax: Exploring the Structure of English, University Press, 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, 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.

• (that contains an identity element): unital

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

• unitary authority
• unitary council
• unitary group (group whose elements are unitary matrices or operators)
• unitary representation

• unitariness
• unitarily
• unitarity

unitary (plural unitaries)

1. (Britain) 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, page 170,

     Can unitaries in a unital C*-algebra with real rank zero be approximated by unitaries with finite spectrum?