unitary

UK /ˈjuːnɪt(ə)ɹi/ US /ˈjuːnɪt(ə)ɹi/
adj 4noun 2

Definitions

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.

2

That concentrates power in a single body, rather than sharing it with more local bodies.

a unitary authority

a unitary state

3

That contains an identity element.

4

Whose inverse is equal to its adjoint.

The eigenvectors of an orthogonal or unitary operator, corresponding to different eigenvalues, are orthogonal.

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.

noun

1

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.

2

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?

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