Linear classical group
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linear_classical_group&oldid=11422
Linear classical group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linear_classical_group&oldid=11422
This article was adapted from an original article by V.L. Popov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article