41 Matrix Groups

Matrix groups are groups generated by invertible square matrices. 

gap> m1 := [ [ Z(3)^0, Z(3)^0,   Z(3) ],
>            [   Z(3), 0*Z(3),   Z(3) ],
>            [ 0*Z(3),   Z(3), 0*Z(3) ] ];;
gap> m2 := [ [   Z(3),   Z(3), Z(3)^0 ],
>            [   Z(3), 0*Z(3),   Z(3) ],
>            [ Z(3)^0, 0*Z(3),   Z(3) ] ];; 
gap> m := Group( m1, m2 );
Group(
[ [ [ Z(3)^0,Z(3)^0,Z(3) ], [ Z(3),0*Z(3),Z(3) ], [ 0*Z(3),Z(3),0*Z(3) ] ], 
  [ [ Z(3),Z(3),Z(3)^0 ], [ Z(3),0*Z(3),Z(3) ], [ Z(3)^0,0*Z(3),Z(3) ] ] ])

  • IsMatrixGroup( grp ) C

    For most operations, GAP only provides methods for finite matrix groups. Many calculations in finite matrix groups are done via a NiceMonomorphism (see Nice Monomorphisms) that represents a faithful action on vectors.

    Sections

    1. Attributes and Properties for Matrix Groups
    2. GL and SL
    3. Invariant Forms
    4. Matrix Groups in Characteristic 0
    5. Acting OnRight and OnLeft

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    GAP 4 manual
    February 2000