Comparisons of Row Spaces
V = W
:true
if the two row spaces V, W are equal as sets,
and false
otherwise.
V < W
:true
if the row space V is smaller than the row space W,
and false
otherwise. The first criteria of this ordering are the
comparison of the fields and the dimensions, row spaces over the same
field and of same dimension are compared by comparison of the
reversed canonical bases (see CanonicalBasis).
Arithmetic Operations for Row Spaces
V + W
:
V / U
:
gap> v:= GF(2)^2; v.name:= "v";; RowSpace( GF(2), [ [ Z(2)^0, 0*Z(2) ], [ 0*Z(2), Z(2)^0 ] ] ) gap> s:= Subspace( v, [ [ 1, 1 ] * Z(2) ] ); Subspace( v, [ [ Z(2)^0, Z(2)^0 ] ] ) gap> t:= Subspace( v, [ [ 0, 1 ] * Z(2) ] ); Subspace( v, [ [ 0*Z(2), Z(2)^0 ] ] ) gap> s = t; false gap> s < t; false gap> t < s; true gap> u:= s+t; Subspace( v, [ [ Z(2)^0, Z(2)^0 ], [ 0*Z(2), Z(2)^0 ] ] ) gap> u = v; true gap> f:= u / s; Subspace( v, [ [ Z(2)^0, Z(2)^0 ], [ 0*Z(2), Z(2)^0 ] ] ) / [ [ Z(2)^0, Z(2)^0 ] ]
GAP 3.4.4