Fwd: [Maxima-lang-fr] Petite question sur le calcul echelon d'une matrice...

-----maxima-bounces at math.utexas.edu wrote: -----

>To: "maxima mailing list" <maxima at math.utexas.edu>
>From: "Robert Dodier" <robert.dodier at gmail.com>
>Sent by: maxima-bounces at math.utexas.edu
>Date: 08/19/2007 08:25PM
>cc: patrick.gelin at free.fr
>Subject: Fwd: [Maxima-lang-fr] Petite question sur le
>calcul     echelon d'une matrice...
>
>Forwarding this message from the French-language mailing list.
>If I understand correctly, the question is, why does Maxima put -5/2
>in the second line of the return value from echelon ?
>It seems like the 2nd line should be unchanged since the
>leading nonzero term is a 1 on the diagonal.

I think that Maxima's answer isn't wrong. It seems that echelon sometimes
does a row swap when it doesn't need to.

(%i72) m : matrix([1,0,-3,1,2],[0,1,-4,-3,1],[-3,2,1,-8,-6],[2,-3,6,7,9]);
(%o72) matrix([1,0,-3,1,2],[0,1,-4,-3,1],[-3,2,1,-8,-6],[2,-3,6,7,9])
(%i73) rowop(m, 3,1, -3)$
(%i74) rowop(%,4,1, 2)$
(%i75) rowswap(%,2,3)$
(%i76) rowop(%,2,2,1/2)$
(%i77) rowop(%,3,2,1)$
(%i78) rowop(%,4,2,-3)$
(%i79) rowop(%,3,3,3)$
(%i80) rowop(%,4,3,-5/2);
(%o80) matrix([1,0,-3,1,2],[0,1,-4,-5/2,0],[0,0,0,1,-2],[0,0,0,0,0])
(%i81) echelon(m);
(%o81) matrix([1,0,-3,1,2],[0,1,-4,-5/2,0],[0,0,0,1,-2],[0,0,0,0,0])

Here is another echelon oddity:

  (%i90) echelon(float(m)), keepfloat : true;
  (%o90) matrix([1,0,-3.0,1.0,2.0],[0,1,-4,-5
  /2,0],[0,0,0,1,-2],[0,0,0,0,0])

Each member of the first row of %o90 is a float, but other rows aren't.

Barton