unexpected condition number of matrix



Hello Barton,

you are right, there is are errors in the math text I am studying, whose caculation I
verify with Maxima:
Gramlich/Werner: Numerische Mathematik mit MatLab, 1.Ed. 2000, page 214.
I will send a mail to the authors ..

Sorry, I should have checked the calculation by my head :-)
so please excuse my sponaneous question and thanks for your help

HTH Wolfgang


"Barton Willis" <willisb at unk.edu> schrieb:
> ----maxima-bounces at math.utexas.edu wrote: -----
> 
> >(%i1) load("linearalgebra");
> >(%i2) B: matrix([3,4],[4,5]);
> >(%i3) mat_cond(B,1);    --> 84
> >(%i4) mat_cond(B,inf);  --> 84
> >
> >which should be 24.
> 
> Why 24? I get(with Maxima 5.11.0
> 
> (%i1) load(linearalgebra)$
> (%i2) B: matrix([3,4],[4,5])$
> (%i3) mat_cond(B,1);
> (%o3) 81
> (%i4) mat_cond(B, 'inf);
> (%o4) 81
> 
> I'm perplexed that you got 84 with Maxima 5.11.0. I also
> don't know why you expected 24 for the infinity norm.
> 
> >I was surprised and calculated the matrix norm (which was also 'wrong')
> 
> What did you get? What did you expect?
> 
> (%i5) mat_norm(B,1);
> (%o5) 9
> (%i6) mat_norm(B,'inf);
> (%o6) 9
> 
> Aren't these OK? row sum = 9 and column sum = 9.
> 
> >and also
> >
> >(%i5) B^^-1;            --> [ 5 -3]
> >                            [-4  3]
> >
> >which I expected to be  1/3* above.
> 
> Why did you expect an additional factor of 1/3? I get
> 
> (%i9) B^^-1;
> (%o9) matrix([-5,4],[4,-3])
> (%i10) %.B;
> (%o10) matrix([1,0],[0,1])
> 
> Also the row and column sums of B^^-1 are 9. So the condition
> number is 81 for both the 1 and infinity norms.
> 
> Barton