58.2 Operations and Attributes for Vector Spaces

For an F-vector space V, GeneratorsOfLeftVectorSpace returns a list of vectors in V that generate V as an F-vector space.

gap> GeneratorsOfVectorSpace( FullRowSpace( Rationals, 3 ) );
[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ]

For a vector space V, TrivialSubspace returns the subspace of V that consists of the zero vector in V.

gap> V:= GF(3)^3;;
gap> triv:= TrivialSubspace( V );
<vector space over GF(3), with 0 generators>
gap> AsSet( triv );
[ [ 0*Z(3), 0*Z(3), 0*Z(3) ] ]

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