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 special linear group - Definition 

General linear group (7754 bytes)
1: ...nary [[matrix multiplication]]. (This is indeed a group because the product of two invertible matrices is...
3: ...'SL''(''n'', ''F'') or ''SL''(''n''), is the [[subgroup]] of ''GL''(''n'', ''F'') consisting of matrices ...
5: ...''. These groups are important in the theory of [[group representation]]s, and also arise in the study of...
7: If ''n'' ≥ 2, then the group ''GL''(''n'', ''F'') is not [[abelian]].
9: ==General linear group of a vector space==

Projective linear group (1933 bytes)
1: ...eld (mathematics)|field]] ''F'' is the [[quotient group]]
3: ...neral linear group]] on ''V'' and Z(''V'') is the group of all nonzero scalar transformations of ''V''.
5: The '''projective special linear group''' is defined analogously:
7: where SZ(''V'') is the group of scalar transformations with unit [[determinant...
9: ...oups Z(''V'') and SZ(''V'') are the [[center of a group|centers]] of GL(''V'') and SL(''V'') respectively...

Linear algebraic group (3603 bytes)
1: ...omial]] equations. An example is the [[orthogonal group]], defined by the relation M<sup>T</sup>M = I whe...
3: ...as the group of points of a real linear algebraic group, essentially by the [[Peter-Weyl theorem]].)
4: ...e [[Picard-Vessiot theory]] did lead to algebraic groups.
6: ..., over the same field. For example the ''additive group'' of an ''n''-dimensional [[vector space]] has a ...
8: ...up> containing the identity will be a [[normal subgroup]] of G.

Special Interest Group (498 bytes)
1: In the [[computer]] field, a '''Special Interest Group''' is a community with a particular interest in a...
4: * [[Bluetooth Special Interest Group]]
7: * [[Special interest]]

Special Patrol Group (1356 bytes)
1: The '''Special Patrol Group''' (SPG) was a controversial unit of the [[London...
5: ...of a disciplined, well-organised team brought the group into increased use for the control of [[protest]]...
11: ... destructive [[hamster]] was named Special Patrol Group by its owner, the [[punk]] character Vyvyan in th...

Special Services Group (615 bytes)
1: ...are, parachute infantry, desert warfare and other specialized units. SSG commandoes are routinely seconded ...

Special unitary group (5172 bytes)
1: ...'), itself a [[subgroup]] of the [[general linear group]] Gl(''n'','''C''').
5: ...y group SU(''n'') is a [[real number|real]] [[Lie group]] of dimension ''n''<sup>2</sup>&minus;1.
6: ...er automorphism group]] of SU(2) is the [[trivial group]].
8: ...] of Lie groups SU(2) &rarr; [[special orthogonal group|SO(3,'''R''')]] whose [[kernel]] is {+'''I''', &m...
12: ...r example, the following matrices form a [[basis (linear algebra)|basis]] for <math>\mathfrak{su}(2)</math...

Bluetooth Special Interest Group (446 bytes)
1: ...th Special Interest Group''' (SIG) is an industry group that standardizes the [[Bluetooth]] system for [[...

Linear B (4083 bytes)
1: [[Image:Linear_B.jpg|thumb|200px|Linear B script sample]]
2: '''Linear B''' is the script that was used for writing [[M...
5: The script was derived from an earlier script ([[Linear A]]) used for writing the [[Minoan]] language and...
9: [[Michael Ventris]] deciphered Linear B in [[1951]]&ndash;[[1953]].
11: Linear B has roughly 200 signs, divided in syllabic sign...

Linear (3480 bytes)
1: ...word '''linear''' comes from the [[Latin]] word ''linearis'', which means ''created by lines''.
3: In [[mathematics]], a '''linear''' [[function (mathematics)|function]] ''f''(''x'...
8: ...h additivity and homogeneity are considered to be linear systems. These two rules, taken together, are oft...
10: ...nes. Although it is possible for a function to be linear and unbounded, these functions are usually of lit...
12: ...n a [[differential equation]] can be expressed in linear form, it is particularly easy to solve by breakin...

Linear A (2190 bytes)
1: ...[Image:Linear_A_tablets_filt.jpg|thumb|left|180px|Linear A etched on tablets found in Akrotiri, [[Santorin...
2: '''Linear A''' is an [[List of undeciphered languages|undec...
4: A related script, [[Linear B]], was deciphered in the [[1950s]] by [[Michael...
6: [[Image:Linear_A_vase_filt.jpg|thumb|right|180px|Linear A etched on a vase, also found in Akrotiri.]]
7: ...[syllable|syllables]] associated with Linear B in Linear A writings produces words that are unrelated to a...

Linear interpolation (4726 bytes)
1: '''Linear interpolation''' is a process employed in [[mathe...
3: ==How to do linear interpolation==
6: <tr><td>[[Image:Linear_interpolation.png]]</td></tr>
27: ==Linear interpolation as approximation==
29: ...typically used to approximate the function ''f''. Linear interpolation can be regarded as a trivial exampl...

Linear prediction (3685 bytes)
1: ...gnal]] are estimated as a [[linear transformation|linear function]] of previous samples.
3: ...ystem analysis]] (a subfield of [[mathematics]]), linear prediction can be viewed as a part of [[mathemati...
17: ...ions are valid for all types of (one-dimensional) linear prediction. The differences are found in the way ...
57: ...umber of multiplications and divisions. It uses a special symmetrical property of parameter vectors on subs...

Piecewise linear (1858 bytes)
1: ...Piecewise]]. There's a lot to say about piecewise-linear (PL) structure and PL morphisms. - msh210 -->
3: In [[mathematics]], a '''piecewise linear''' function
8: ...]] [[polytope]]s, such that ''f'' is equal to a [[linear function]] on each of these polytopes.
10: ... <math>[x_1,x_2]</math>. Then ''f'' is piecewise linear
12: sub-interval ''I'', ''f'' is equal to a linear function

Linear classifier (266 bytes)
1: ...inear classifier''' is a classifier that uses a [[linear function]] of its inputs to base its decision on.
4: * [[Fisher's linear discriminator]]

Linear Flash (1504 bytes)
1: ...] format now used primarily in Cisco [[router]]s. Linear Flash requires no battery support, unlike somewha...
3: ...]s) and prohibitive costs; megabyte-for-megabyte, Linear Flash cards are often dozens of times more expens...
5: Linear Flash cards begin to develop bad blocks after abo...
7: Linear Flash cards were also the primary method of data ...
9: .... [[Intel]], which championed the adoption of the Linear Flash format, also manufactured cards.

Linear animal (373 bytes)
1: '''Linear animals''' are animals which are very close to ea...

Linear perspective (3814 bytes)
1: '''Linear perspective''' is the [[art]] of representing thr...
12: If the viewpoint is pointing directly into a linear object like a building or a road, one would use o...
22: *[[curvilinear perspective]]

What is linear aeration (1020 bytes)
1: '''What is linear aeration? '''
3: ...and, clay etc)if necessary. The other property of Linear Aeration is to alleviate excessive water of turf ...
5: The process of Linear aeration consists of adding the necessary organic...
7: '''Linear aeration provides:'''

Linear programming (7888 bytes)
1: ...tive function]] and the [[constraints]] are all [[linear]].
3: ...oblems as sub-problems. Historically, ideas from linear programming have inspired many of the central con...
6: ... plant with wheat vs barley can be expressed as a linear programming problem:
29: ...ocal optima are automatically global optima. The linear objective function also implies that an optimal s...
38: ...fact for some time it was not known whether the [[linear programming]] problem was [[NP-complete]] or poly...

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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "special linear group".