• A linear group is a group that is isomorphic to a matrix group (that is, admitting a faithful, finite-dimensional representation over K).
  • The set of all such invertible linear transformations from the vector space Rn to itself is called the General Linear group and is denoted by GL(n, R) or GLn(R)...
  • Over any field K, linear group usually refers to an algebraic group which is a (Zariski closed) subgroup of the general linear group GL(n,K)...
  • The general linear group over , denoted GL(V) , is the group of all vector space automorphisms from to itself.
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  • Among infinite groups, linear groups form an interesting and tractable class. Examples of groups that are not linear include groups which are "too big"...
  • The colimit over this diagram in the category of topological group is called the stable general linear group denoted.
  • sage: SL(2, ZZ) Special Linear Group of degree 2 over Integer Ring sage: G = SL(2, GF(3)); G Special Linear Group of degree 2 over Finite Field of size 3.
  • and different fields. F. . The general linear group is an algebraic group, and it is a Lie group if. V. is a real or complex vector space.
  • In mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication.