Basis( V )
Basis( V, vectors )
Basis( V )
returns a basis of the row space V. If the component
V.canonicalBasis
or V.semiEchelonBasis
was bound before the first
call to Basis
for V then one of these bases is returned. Otherwise a
semi-echelonized basis (see Row Space Bases) is computed.
The basis is stored in V.basis
.
Basis( V, vectors )
returns the basis of V that consists of the
vectors in the list vectors. In the case that V.basis
was not bound
before the call the basis is stored in this component.
Note that it is not necessarily checked whether vectors is really linearly independent.
gap> v:= GF(2)^2; v.name:= "v";; RowSpace( GF(2), [ [ Z(2)^0, 0*Z(2) ], [ 0*Z(2), Z(2)^0 ] ] ) gap> b:= Basis( v, [ [ 1, 1 ], [ 1, 0 ] ] * Z(2) ); Basis( v, [ [ Z(2)^0, Z(2)^0 ], [ Z(2)^0, 0*Z(2) ] ] ) gap> Coefficients( b, [ 0, 1 ] * Z(2) ); [ Z(2)^0, Z(2)^0 ] gap> IsSemiEchelonBasis( b ); false
GAP 3.4.4