The bug is apparently in $SAGE_ROOT/devel/sage/sage/matrix2.pyx,
in _echelon_in_place_classical
indeed:

sage: m=matrix(2,[1.5,1.75,-1.5,-1.75])
sage: set_verbose(10)
sage: m.rank()
verbose 1 (<module>) generic in-place Gauss elimination on 2 x 2
matrix
verbose 1 (<module>) done with gauss echelon form (time = 0.0)
2

(m.rank() delegates to _echelon_in_place_classical() in this case)

On Aug 17, 2:20 pm, vgermrk <vger...@googlemail.com> wrote:
> I discussed the following issue with <logix> @IRC:
>
> sage: rank(matrix(2,[1.5,1.75,-1.5,-1.75]))
> 2
>
> gives a wrong answer.
>
> Multiplying with a full rank matrix also gives unexpected results:
>
> sage:  rank( matrix(2,2,[1,0,0,1]) * matrix(2,[1.5,1.75,-1.5,-1.75]) )
> 2
> sage:  rank( matrix(2,2,[1,0,1,1]) * matrix(2,[1.5,1.75,-1.5,-1.75]) )
> 1
>
> And even more serious: multiplying with another rank one matrix:
>
> sage:  rank( matrix(2,2,[1,0,1,0]) * matrix(2,[1.5,1.75,-1.5,-1.75]) )
> 2
>
> I think this is something that should be fixed.
> -vgermrk-

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