Editing Group theory (section)

===Matrix groups===
The next important class of groups is given by ''matrix groups'', or [[linear group]]s. Here ''G'' is a set consisting of invertible [[matrix (mathematics)|matrices]] of given order ''n'' over a [[field (mathematics)|field]] ''K'' that is closed under the products and inverses. Such a group acts on the ''n''-dimensional vector space ''K''<sup>''n''</sup> by [[linear transformation]]s. This action makes matrix groups conceptually similar to permutation groups, and the geometry of the action may be usefully exploited to establish properties of the group ''G''.