41.1 Attributes and Properties for Matrix Groups

  • DimensionOfMatrixGroup( mat-grp ) A

    The dimension of the matrix group.

  • DefaultFieldOfMatrixGroup( mat-grp ) A

    Is a field containing all the matrix entries. It is not guaranteed to be the smallest field with this property.

  • FieldOfMatrixGroup( matgrp ) A

    The smallest field containing all the matrix entries of all elements of the matrix group matgrp. As the calculation of this can be hard, this should only be used if one really needs the smallest field, use DefaultFieldOfMatrixGroup to get (for example) the characteristic. 

    gap> DimensionOfMatrixGroup(m);
3
gap> DefaultFieldOfMatrixGroup(m);
GF(3)

  • TransposedMatrixGroup( matgrp ) A

    returns the transpose of the matrix group matgrp. The transpose of the transpose of matgrp is identical to matgrp. 

    gap> G := Group( [[0,-1],[1,0]] );
Group([ [ [ 0, -1 ], [ 1, 0 ] ] ])
gap> T := TransposedMatrixGroup( G );
Group([ [ [ 0, 1 ], [ -1, 0 ] ] ])
gap> IsIdenticalObj( G, TransposedMatrixGroup( T ) );
true

  • ProjectiveActionOnFullSpace( G, f, n ) F

    returns the image of the projective acion of G on f n , which must be finite.

  • ProjectiveActionHomomorphismMatrixGroup( G ) F

    returns an action homomorphism for a faithful projective action of G on the underlying vector space. (Note: The action is not necessarily on the full space, if a smaller subset can be found on which the action is faithful.)

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    GAP 4 manual
    February 2000