Matrix Groups

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(n1)/2.

definition (Special Orthogonal Group):

SOn(R)={A | AAt=I}=ker(GLn(R)k×).

definition (Unitary Group):

Un(C):={A | AA=AA=1}.

definition (Special Unitary Group):

SUn(C):={AUn(C) | detA=1}.

definition (Symplectic Group):

Sp2n(C):={AGL2n(C) | AtJA=J}J:=[01n1n0].

\todo[inline]{Matrix group definitions.}