linear group

English

Noun

linear group (plural linear groups)

1. (group theory) Any group that is isomorphic to a matrix group.
   • 2003, Paul M. Cohn, Further Algebra and Applications, Springer, page 116:

     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).

   • 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.

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

     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.

Derived terms

• general linear group
• special linear group

Translations

group isomorphic to a matrix group

See also

• linear algebraic group