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单词 matrix groups
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 groupthe 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.

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更新时间:2025/4/29 8:09:29