special linear group
Given a vector space V, the special linear group SL(V) is defined to be the subgroup of the general linear group GL(V) consisting of all invertible linear transformations T:V⟶V in GL(V) that have determinant 1.
If V=𝔽n for some field 𝔽, then the group SL(V) is often denoted SL(n,𝔽) or SLn(𝔽), and if one identifies each linear transformation with its matrix with respect to the standard basis, then SL(n,𝔽) consists of all n×n matrices with entries in 𝔽 that have determinant 1.
Title | special linear group |
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Canonical name | SpecialLinearGroup |
Date of creation | 2013-03-22 12:25:38 |
Last modified on | 2013-03-22 12:25:38 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 7 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 20G15 |
Synonym | SL |
Related topic | GeneralLinearGroup |
Related topic | Group |
Related topic | UnimodularMatrix |