unitary

Etymology

adj

1. Having the quality of oneness.
   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. 2004, Andrew Radford, Minimalist Syntax: Exploring the Structure of English, Cambridge, UK: Cambridge University Press, page 221
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.
   The eigenvectors of an orthogonal or unitary operator, corresponding to different eigenvalues, are orthogonal. 1997, P. K. Suetin, Alexandra I. Kostrikin, Yuri I. Manin, translated by M. E. Alferieff, Linear Algebra and Geometry, page 137
   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. 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
   We then repeat the same procedure to the (d − 1) × (d − 1) block unitary matrix using (d − 2) two-level unitary matrices. 2008, Mikio Nakahara, Tetsuo Ohmi, Quantum Computing: From Linear Algebra to Physical Realizations, page 84

noun

1. (UK) A unitary council.
   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. 2005, John Greenwood, Robert Pyper, David Wilson, New Public Administration in Britain
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.
   Can unitaries in a unital C*-algebra with real rank zero be approximated by unitaries with finite spectrum? 2001, Huaxin Lin, An Introduction to the Classification of Amenable C*-Algebras, page 170