Basis( V )
Basis( V, vectors )
Basis( V ) returns a basis of the row space V. If the component
V.semiEchelonBasis was bound before the first
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
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
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