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.

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