# 33.6 RowSpace

`RowSpace( F, generators )`

returns the row space that is generated by the vectors generators over the field F. The elements in generators must be GAP vectors.

`RowSpace( F, generators, zero )`

Whenever the list generators is empty, this call of `RowSpace` has to be used, with zero the zero vector of the space.

`RowSpace( F, generators, "basis" )`

also returns the F-space generated by generators. When the space is constructed in this way, the vectors generators are assumed to form a basis, and this is used for example when `Dimension` is called for the space.

It is not checked that the vectors are really linearly independent.

`RowSpace( F, dimension )`
`F ^ n`

return the full row space of dimension n over the field F. The elements of this row space are all the vectors of length n with entries in F.

```    gap> v1:= RowSpace( GF(2), [ [ 1, 1 ], [ 0, 1 ] ] * Z(2) );
RowSpace( GF(2), [ [ Z(2)^0, Z(2)^0 ], [ 0*Z(2), Z(2)^0 ] ] )
gap> v2:= RowSpace( GF(2), [], [ 0, 0 ] * Z(2) );
RowSpace( GF(2), [ [ 0*Z(2), 0*Z(2) ] ] )
gap> v3:= RowSpace( GF(2), [ [ 1, 1 ], [ 0, 1 ] ] * Z(2), "basis" );
RowSpace( GF(2), [ [ Z(2)^0, Z(2)^0 ], [ 0*Z(2), Z(2)^0 ] ] )
gap> v4:= RowSpace( GF(2), 2 );
RowSpace( GF(2), [ [ Z(2)^0, 0*Z(2) ], [ 0*Z(2), Z(2)^0 ] ] )
gap> v5:= GF(2) ^ 2 ;
RowSpace( GF(2), [ [ Z(2)^0, 0*Z(2) ], [ 0*Z(2), Z(2)^0 ] ] )
gap> v3 = v4;
true ```

Note that the list of generators may contain zero vectors.

GAP 3.4.4
April 1997