| 释义 |
matrix groups A term loosely applying to groups of matrices under matrix multiplication, particularly important in geometry. Examples include:
| GL(n,F) | The general linear group. Invertible n × n matrices with entries in the field F. | | SL(n,F) | The special linear group. Determinant 1 n × n matrices with entries in F. | | O(n) | orthogonal n × n matrices. | | SO(n) | orthogonal n × n matrices with determinant 1. | | U(n) | unitary n × n matrices. | | SU(n) | unitary n × n matrices with determinant 1. | | AGL(n,F) | affine transformations on Fn. | | PGL(n,F) | projective transformations on n–1 dimensional projective space over F. | | Lorentz group | the linear isometries (see linear map) of Minkowski space. | | Sp(2n,F) | sympletic group of those 2n × 2n matrices M over F satisfying MTΩM = Ω, where

|
See also Lie groups, linear groups. |