linear group

plural linear groups

1. group theoryAny group that is isomorphic to a matrix group.

   The standard examples are linear groups such as the orthogonal and unitary groups, or the additive groups of p-adic integers, and this confirms that the concept of a compact group is natural.

   2007, Karl Heinrich Hofmann, Sidney A. Morris, The Lie Theory of Connected Pro-Lie Groups, European Mathematical Society, page 1

   2 more examples

   In this section we shall describe the linear groups and in the next two sections we deal with the symplectic and orthogonal groups, collectively usually known under the name of classical groups since the time of Hermann Weyl (1939).

   2003, Paul M. Cohn, Further Algebra and Applications, Springer, page 116

   2007, Peter Schmid, The Solution of the k(GV) Problem, Imperial College Press, page vii, So finite groups often appear as subgroups of permutation groups or linear groups. The “geometry” of a group (as permutation group or linear group, or as a group of Lie type etc.) should be used in order to describe basic invariants.