[GAP Forum] A small question about matrices

[Igor Korepanov]

Dear GAP maintainers,

If I am right, the CanonicalBasis command for vector spaces in a situation like this:

gap> A := [ [1,2,3], [4,5,6], [7,8,9] ];                    
[ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ] ]
gap> BasisVectors( CanonicalBasis( VectorSpace( Rationals, A ) ) );
[ [ 1, 0, -1 ], [ 0, 1, 2 ] ]

builds exactly the same matrix as TriangulizeMat, save that zero row(s) is/are stripped off:

gap> TriangulizeMat( A );;   A;
[ [ 1, 0, -1 ], [ 0, 1, 2 ], [ 0, 0, 0 ] ]

My question is: could you confirm that this is firmly so?

Best wishes, 

Igor