Linear classical group

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A group of non-singular linear transformations of a finite-dimensional vector space over a skew-field that is a classical group (see also Linear group). The most important types of linear classical groups are the following: the general linear group , the special linear group and the unitary group (where and is a Hermitian or skew-Hermitian form on , relative to an involution of ). When is also commutative, special important cases are: the symplectic group and the orthogonal group ( a quadratic form on and of characteristic not 2).

How to Cite This Entry:
Linear classical group. V.L. Popov (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098