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单词 SpecialLinearGroup
释义

special linear group


Given a vector spaceMathworldPlanetmath V, the special linear groupMathworldPlanetmath SL(V) is defined to be the subgroupMathworldPlanetmathPlanetmath of the general linear groupMathworldPlanetmath GL(V) consisting of all invertible linear transformations T:VV in GL(V) that have determinantMathworldPlanetmath 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.

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更新时间:2025/5/4 4:03:51