Given a ring 
with identity, the general linear group 
is the group of 
invertible matrices with elements in 
.
The general linear group 
is the set of 
matrices with entries in the field 
which have nonzero determinant.
General Linear Group
See also
Langlands Reciprocity, Projective General Linear Group, Projective Special Linear Group, Special Linear GroupPortions 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
, 
, 
, and 
." §2.1 in Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, p. x, 1985.Referenced on Wolfram|Alpha
General Linear GroupCite this as:
Terr, David and Weisstein, Eric W. "General Linear Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GeneralLinearGroup.html