Unitary matrix (1841 bytes)
1: ...[[complex number|complex]] [[matrix (mathematics)|matrix]] <var>U</var> satisfying the condition
5: ... a matrix ''U'' is unitary if it has an [[inverse matrix|inverse]] which is equal to its conjugate transpo...
7: ... an [[orthogonal matrix]]. Just as an orthogonal matrix ''G'' preserves the (real) [[inner product]] of t...
9: so also a unitary matrix ''U'' satisfies
11: ...product]] on '''C'''^''n''. A matrix is unitary if and only if its columns form an [[orthonormal ...

Unitary (169 bytes)
2: *[[Unitary state]]
5: *[[Unitary matrix]]
6: *[[Unitary operator]]
7: *[[Unitary group]]
8: *[[Unitary representation]]

Unitary group (1171 bytes)
2: ...es from ''F'', with the group operation that of [[matrix multiplication]]. This is a [[subgroup]] of the [...
4: ...plex plane, under multiplication. All the complex unitary groups contain copies of this group.
6: ...mplex numbers one usually writes U(''n'') for the unitary group of degree ''n''.
8: The unitary group U(''n'') is a ''real'' [[Lie group]] of dim...
10: ''See also'': [[Special unitary group]]

Unitary equivalence (194 bytes)
1: *For '''unitary equivalence''' of [[bounded operator]]s in [[Hilb...
2: *For '''unitary equivalence''' of [[unitary representation]]s see that page.

Unitary authority (4024 bytes)
1: A '''unitary authority''' is a term used in a two-tier local g...
5: ...ham Islands Council]] is not usually considered a unitary authority, although it is considered a regional c...
15: ...in [[1974]]. It was not until the [[1990s]] that unitary authorities would be created in the UK.
17: ===Creation of unitary authorities===
19: ...ganisation; and the [[Isle of Wight]], (the first Unitary Authority created after the 1992 Act, and arguabl...

Unitary state (5163 bytes)
1: ...nd mayors ("[[devolved government]]"), but in a ''unitary state'' the central government has the principal ...
3: ... central government is known as ''devolution.'' A Unitary state can broaden and narrow the functions of suc...
5: ...d]] may be given as an example of the opposite, a unitary state lacking [[Subnational entity|subnational]] ...
7: ...that have their own constitutional existence, but unitary with respect to the two mainland territories (the...
9: ... most (if not all) [[U.S. state]]s are themselves unitary, with [[counties]] and other [[municipalities]] h...

Unitary transform (520 bytes)
1: ...ormation]] that can be represented by a [[unitary matrix]].
3: Informally, a unitary transform changes the representation of a vector ...

Unitary transformation (284 bytes)
1: ...[[antiisomorphism]]; that corresponds to an [[antiunitary]] transformation) between two [[Hilbert space]]s ...
3: See also [[unitary matrix]], [[unitary operator]]

Unitary representation (3310 bytes)
1: ...ilbert space]] ''V'' such that &pi;(''g'') is a [[unitary operator]] for every ''g'' &isin; ''G''. The gene...
3: ... unitary representations of ''G'' makes up its '''unitary dual'''. This set can be identified to the [[spe...
5: ...e by the [[Peter-Weyl theorem]]; in that case the unitary dual is a [[discrete space]], and the measure att...
7: ... the pioneers in constructing a general theory of unitary representations was [[George Mackey]].
13: ...''H'' is a group homomorphism from ''G'' into the unitary group of ''H'',

Unitary operator (820 bytes)
1: In [[functional analysis]], a '''unitary operator''' is a [[bounded linear operator]] ''U'...
12: ...or is a generalisation of the notion of a unitary matrix.
14: Unitary operators implement [[isomorphism]]s between [[op...
19: [[Category:Unitary operators]]

Unitary perfect number (668 bytes)
1: ...teger]] which is the sum of its positive proper [[unitary divisor]]s, not including the number itself.
3: ... 1 + 3 + 4 + 5 + 12 + 15 + 20 = 60. The first few unitary perfect numbers are
7: ...own whether or not there are infinitely many even unitary perfect numbers.

Special unitary group (5172 bytes)
1: ...ten as SU(''n''). This is a [[subgroup]] of the [[unitary group]] U(''n''), itself a [[subgroup]] of the [[...
5: The special unitary group SU(''n'') is a [[real number|real]] [[Lie g...
10: ...k{su}(n)</math>. It consists of the [[trace of a matrix|traceless]] [[antihermitian]] ''n''&times;''n'' c...
13: :<math>i\sigma_x = \begin{bmatrix}
15: i & 0 \end{bmatrix}</math>

Unitary Democratic Coalition (Portugal) (251 bytes)
1: The '''Unitary Democratic Coalition''' (Portuguese: '''''Coliga...

Unitary representations of a star Lie superalgebra (1627 bytes)
5: A '''[[unitary representation]]''' of such a Lie algebra is a <b...
7: ...</b> is the unitary rep and also, <b>H</b> is a [[unitary representation]] of A.

Stone's theorem on one-parameter unitary groups (2503 bytes)
1: ...rem''' on [[one-parameter group|one-parameter]] [[unitary]] groups is a basic theorem of [[functional analy...
2: of unitary operators
14: ... referred to as strongly continuous one-parameter unitary groups. The theorem is named after [[Marshall St...
22: is a strongly continuous one-parameter family of unitary operators. The [[infinitesimal generator]] of {'...
30: is a one-parameter unitary group of unitary operators; the infinitesimal generator of this fa...

Matrix (4171 bytes)
1: ...h is ''mater''. Various disciplines use the term "matrix" with differing meanings:
5: * In [[mathematics]], a '''[[Matrix (mathematics)|matrix]]''' is a rectangular table of data.
6: * In [[computer programming]], a '''matrix''' is a 2-dimensional [[array]].
7: ...chondrion]]. See '''[[matrix (biology)|biological matrix]]'''.
8: ...nes. is called a '''[[matrix (geology)|geological matrix]]'''.

The Matrix (26275 bytes)
1: ... The Matrix. For other usages of the term, see [[Matrix]].''
3: [[Image:Matrix-DVD.jpg|right|The Matrix DVD case cover]]
5: '''''The Matrix''''' is a [[film]] first released in the [[United...
9: ==The Matrix series and franchise==
11: ...e provides free comics, set in the world of ''The Matrix''. Some of these comics are now available in prin...

S matrix (1873 bytes)
1: ...S" stands for "scattering" or "Strahlung" in '''S-matrix'''.
3: ...of the [[inhomogeneous]] [[Lorentz group]]; the S-matrix is the [[evolution operator]] between time equal ...
5: ... elements (individual numerical entries) in the S-matrix are known as '''scattering amplitudes'''.
7: ... cases, the [[perturbative]] calculation of the S-matrix leads to [[Feynman diagram]]s.
11: ...ring]] for an example of the application of the S-matrix.

Zero matrix (262 bytes)
1: ..., a '''zero matrix''' is a [[matrix (mathematics)|matrix]] with all its entries being zero. There are zero...

(0,1)-matrix (1004 bytes)
1: ...or '''(0,1)-matrix''' is a [[matrix (mathematics)|matrix]] whose entries are all either zero or one.
7: :<math>\begin{pmatrix}
10: \end{pmatrix}</math> is a 2×2 binary matrix.
12: * A [[permutation matrix]] is a binary matrix, all of whose columns and rows each have exactly ...
13: ... matrix]] in [[analysis of variance]] is a binary matrix with constant row sums.

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