definition (General Linear Group):
GLn(R)={A | A=¯A}.
proposition (Order of GLn):
\todo[inline]{todo}
definition (Special Linear Group):
SLn(C):={A | detA=1}.
definition (Orthogonal Group):
On(C):={A | AtA=AAt=I}.
Dimension: n(n−1)/2.
definition (Special Orthogonal Group):
SOn(R)={A | AAt=I}=ker(GLn(R)→k×).
definition (Unitary Group):
Un(C):={A | A†A=AA†=1}.
definition (Special Unitary Group):
SUn(C):={A∈Un(C) | detA=1}.
definition (Symplectic Group):
Sp2n(C):={A∈GL2n(C) | AtJA=J}J:=[01n1n0].
\todo[inline]{Matrix group definitions.}