General Linear Group

Given a ring R with identity, the general linear group GL_n(R) is the group of n×n invertible matrices with elements in R.

The general linear group GL_n(q) is the set of n×n matrices with entries in the field F_q which have nonzero determinant.

See also

Langlands Reciprocity, Projective General Linear Group, Projective Special Linear Group, Special Linear Group

Portions of this entry contributed by David Terr

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References

Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. "The Groups GL_n(q), SL_n(q), PGL_n(q), and PSL_n(q)=L_n(q)." §2.1 in Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, p. x, 1985.

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General Linear Group

Cite this as:

Terr, David and Weisstein, Eric W. "General Linear Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GeneralLinearGroup.html

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