Re: [Maxima-discuss] uniteigenvectors does not return unit vectors (5.37.3)

[Michel T. <ta...@lp...>]

Le 16/01/2017 à 12:05, Soegtrop, Michael a écrit :
> (%i2) a:matrix([1,7,3],[7,4,-5],[3,-5,6]);
>
> (%o2) matrix([1,7,3],[7,4,-5],[3,-5,6])
>
> (%i3) load(eigen);
>
> (%o3) "C:/Program Files
> (x86)/Maxima-sbcl-5.37.3/share/maxima/5.37.3/share/matrix/eigen.mac"
>
> (%i7) evecsu:rectform(float(uniteigenvectors(a)))$
>
> (%i8) evec2:evecsu[2][2][1];
>
> (%o8)
> [0.993506133354939,-8.326672684688674*10^-17*%i-0.8915008009299733,1.087133163311995*10^-16*%i-0.5718068323676483]
>
> (%i10) rectform(evec2.evec2);
>
> (%o10) 2.413867325458305*10^-17*%i+2.10879116861499
>
>
>
> So this results in 2.10879116861499 rather than 1.
>
>
>
> I tested this on Maxima 5.37.3.
>

Here i tested this on maxima 5.39.0 and it doesn't work at all. I get

eigenvectors: the eigenvector(s) for the 1 th eigenvalue will be missing.

eigenvectors: the eigenvector(s) for the 2 th eigenvalue will be missing.

eigenvectors: the eigenvector(s) for the 3 th eigenvalue will be missing.

When computing the eigenvalues with bfloats and fpprec:30 one sees that
they are all real and are:
7.03594584795763099344518048443b0
- 7.00792852354785898506814578269b0
1.09719826755902279916229652983b1
so we are in the case where the 3rd degree equation has 3 real solutions 
which can only be expressed as complex formulas. Apparently this 
confuses eigenvector.

One can find the eigenvalues numerically like this: for the first one:
X:[x,y,z]$
Y:a.X-7.03594584795763099344518048443b0*X$
solve([Y[1,1],Y[2,1]],[x,y])
float(solve(subst(%[1],x^2+y^2+z^2=1)));
gives z = 0.7449388486979633 for z>0 and then
x = 0.6287841861843084, y = 0.2229272502523859
so there is no real problem computing this normalized eigenvector. Which 
means there is a bug in "eigenvectors". Slightly deforming the matrix a 
above leaves the same error.





-- 
Michel Talon