The transform is sometimes denoted by the symbol, as in or or < ref group =" note "> As a linear transformation on a finite-dimensional vector space, the DFT expression can also be written in terms of a DFT matrix ; when scaled appropriately it becomes a unitary matrix and the X < sub > k </ sub > can thus be viewed as coefficients of x in an orthonormal basis .</ ref >

For example Sp ( 8 ) has a representation in terms of 4x4 quaternion unitary matrices which has a 16 dimensional real representation and so might be considered as a candidate for a gauge group.

For general nonabelian locally compact groups, harmonic analysis is closely related to the theory of unitary group representations.

This is the Lie algebra of the unitary group U ( n ).

Unitary matrices of determinant 1 form a closed connected subgroup of dimension n < sup > 2 </ sup > − 1 denoted SU ( n ), the special unitary group.

A quantum description consists of a Hilbert space of states, observables are self adjoint operators on the space of states, time evolution is given by a one-parameter group of unitary transformations on the Hilbert space of states, and physical symmetries are realized by unitary transformations.

Alternatively, by Stone's theorem one can state that there is a strongly continuous one-parameter unitary group U ( t ): H → H such that

Similar equations can be written for any one-parameter unitary group of symmetries of the physical system.

Time would be replaced by a suitable coordinate parameterizing the unitary group ( for instance, a rotation angle, or a translation distance ) and the Hamiltonian would be replaced by the conserved quantity associated to the symmetry ( for instance, angular or linear momentum ).

Other branches lacking any trace of the noun-class system are Dogon and Ijaw, whereas the Talodi branch of Kordofanian does have cognate noun classes, suggesting that Kordofanian is also not a unitary group.

When it becomes possible for a people to describe as ‘ postmodern ’ the décor of a room, the design of a building, the diegesis of a film, the construction of a record, or a ‘ scratch ’ video, a television commercial, or an arts documentary, or the ‘ intertextual ’ relations between them, the layout of a page in a fashion magazine or critical journal, an anti-teleological tendency within epistemology, the attack on the ‘ metaphysics of presence ’, a general attenuation of feeling, the collective chagrin and morbid projections of a post-War generation of baby boomers confronting disillusioned middle-age, the ‘ predicament ’ of reflexivity, a group of rhetorical tropes, a proliferation of surfaces, a new phase in commodity fetishism, a fascination for images, codes and styles, a process of cultural, political or existential fragmentation and / or crisis, the ‘ de-centring ’ of the subject, an ‘ incredulity towards metanarratives ’, the replacement of unitary power axes by a plurality of power / discourse formations, the ‘ implosion of meaning ’, the collapse of cultural hierarchies, the dread engendered by the threat of nuclear self-destruction, the decline of the university, the functioning and effects of the new miniaturised technologies, broad societal and economic shifts into a ‘ media ’, ‘ consumer ’ or ‘ multinational ’ phase, a sense ( depending on who you read ) of ‘ placelessness ’ or the abandonment of placelessness (‘ critical regionalism ’) or ( even ) a generalised substitution of spatial for temporal coordinates-when it becomes possible to describe all these things as ‘ Postmodern ’ ( or more simply using a current abbreviation as ‘ post ’ or ‘ very post ’) then it ’ s clear we are in the presence of a buzzword.

( See Special unitary group.

For solvable groups, Hall's theorems assert the existence of a subgroup of order equal to any unitary divisor of the group order ( that is, a divisor coprime to its cofactor ).

Ladin ( ), is a language consisting of a group of dialects ( which some consider part of a unitary Rhaeto-Romance language ) spoken in the Dolomite Mountains in Northern Italy in the border regions of the provinces Trentino, South Tyrol and Belluno.

The group manifold GL ( n, C ) is not compact ; rather its maximal compact subgroup is the unitary group U ( n ).

* unitary group, U ( V ), which, when F = C, preserves a non-degenerate hermitian form on V.

* For any positive integer n, the set of all n by n unitary matrices with matrix multiplication forms a group, called the unitary group U ( n ).

Alternatively, we could control the Hamiltonian of the system, and thus the time evolution operator U ( for a time independent Hamiltonian,, where is called the generator of translations in time ) up to some fixed time interval, which yields a unitary operator.

Since U is unitary, it preserves the inner product:

Subsequent to the use of congress by the U. S. legislature, the term has been adopted by many states within unions, and by unitary nation-states in the Americas, to refer to their legislatures.

In the South West region the following transport authorities have published their LTP online: Bournemouth U. A., Cornwall U. A., Devon, Dorset, Gloucestershire, Plymouth U. A., Somerset, Swindon U. A., Torbay U. A. and Wiltshire unitary authority.

We are provided with ( quantum black box ) access to a subroutine in the form of a unitary operator, U < sub > ω </ sub >, which acts as:

SVD of matrix A computes unitary matrices U and V and a rectangular diagonal matrix S of the same size as A with nonnegative diagonal entries, such that

i. e., U is unitary and such that

NU for some unitary U. ( See square root of a matrix for more details.

The Hamiltonian gives the rate at which the particle has an amplitude to go from m to n. The reason it is multiplied by i is that the condition that U is unitary translates to the condition:

In mathematics, a complex square matrix U is unitary if

For any unitary matrix U, the following hold:

# U is unitary

# U * is unitary

where U is an m × m real or complex unitary matrix, Σ is an m × n rectangular diagonal matrix with nonnegative real numbers on the diagonal, and V * ( the conjugate transpose of V ) is an n × n real or complex unitary matrix.

Judicial power is exercised by the judiciary, consisting of the Supreme Court of Justice of the Nation, the Council of the Federal Judiciary and the collegiate, unitary and district tribunals.

The subgroup of the unitary group consisting of matrices of determinant 1 is called the special unitary group and denoted SU ( n, q ) or SU ( n, q² ).

The special unitary group is a subgroup of the unitary group U ( n ), consisting of all n × n unitary matrices, which is itself a subgroup of the general linear group GL ( n, C ).

( For those who were first introduced to dual groups consisting of characters which are the continuous homomorphisms into the circle group, this approach is similar except that the circle group is ( ultimately ) generalised to the group of unitary operators on a given Hilbert space.

To state the third and final part of the theorem, there is a natural Hilbert space over G consisting of square-integrable functions, L < sup > 2 </ sup >( G ); this makes sense because Haar measure exists on G. Calling this Hilbert space H, the group G has a unitary representation ρ on H by acting on the left, via

In the Redcliffe-Maud Report no directly-analogous area had been proposed, with the part north of the Humber consisting of one unitary authority, and the part south of it constituting another.

During a further local government review in the 2000s as part of the preparations for the regional assembly referendums, a North Riding of Yorkshire unitary authority consisting of Richmondshire, Hambleton, Ryedale and Scarborough was again suggested.

Bristol, Herefordshire, Isle of Wight, Northumberland and Rutland are ceremonial counties consisting of a non-metropolitan county of a single district, and are known as unitary authorities.

A unitary authority, also named Flintshire, was formed in 1996 under the Local Government ( Wales ) Act 1994, consisting only of the Alyn and Deeside and Delyn districts-the Wrexham Maelor parts now form part of Wrexham County Borough, with the former Rhuddlan district forming the northernmost part of the current Denbighshire unitary authority.

* In the case of the special unitary group SU ( n ), the n − 1 fundamental representations are the wedge products consisting of the alternating tensors, for k = 1, 2, ..., n − 1.

*** In 1996, the then new unitary Highland Council adopted the areas of the eight districts of the former two-tier Highland region as management areas, and each management area was represented, initially, by area committees consisting of councillors elected from areas ( groups of wards ) corresponding to the management areas, but changes to ward boundaries in 1999 created a mismatch between committee areas and management areas.

Two options were proposed by the Boundary Committee for each county in the review area-generally consisting of a single unitary authority for the entire county, or a breakup into smaller authorities which are larger than the existing districts.

The Lord Lieutenant of Angus, is the British monarch's personal representative in an area which was defined by the Lord-Lieutenants ( Scotland ) Order 1996 as consisting of the unitary Angus council area, in Scotland.

The constituency covers part of the South Gloucestershire unitary authority, consisting of the eastern suburbs of Bristol outside of the city boundary, including the town of Kingswood itself.

According to it, Peoples Republic of Bangladesh is a unitary republic consisting of the territories of the former East Pakistan and also included territories ( some enclaves exchanged with India ).