9.1 VectorSpace

`VectorSpace( generators, field )`

Let generators be a list of objects generating a vector space over the field field. Then `VectorSpace` returns this vector space represented as a GAP record.

```    gap> f := GF( 3^2 );
GF(3^2)
gap> m := [ [ f.one, f.one ], [ f.zero, f.zero ] ];
[ [ Z(3)^0, Z(3)^0 ], [ 0*Z(3), 0*Z(3) ] ]
gap> n := [ [ f.one, f.zero ], [ f.zero, f.one ] ];
[ [ Z(3)^0, 0*Z(3) ], [ 0*Z(3), Z(3)^0 ] ]
gap> VectorSpace( [ m, n ], f );
VectorSpace( [ [ [ Z(3)^0, Z(3)^0 ], [ 0*Z(3), 0*Z(3) ] ],
[ [ Z(3)^0, 0*Z(3) ], [ 0*Z(3), Z(3)^0 ] ] ], GF(3^2) ) ```

`VectorSpace( generators, field, zero )`

`VectorSpace` returns the vector space generated by generators over the field field having zero as the uniquely determined neutral element. This call of `VectorSpace` always is requested if generators is the empty list.

```    gap> VectorSpace( [], f, [ [ f.zero, f.zero ], [ f.zero, f.zero ] ] );
VectorSpace( [  ], GF(3^2), [ [ 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3) ]
] ) ```

GAP 3.4.4
April 1997