As far as I can tell, the problem is that you use the predefined i which is a symbolic constant rather than a numerical one. (Maybe someone else can elaborate on this.)
Here are some ways you can get the right answer: 1. declare i explicitly to be a complex number: sage: A=matrix([[-1,-1+CC(i)],[1,0]]) sage: A.eigenvalues() [1.00000000000000*I, -1.00000000000000 - 1.00000000000000*I] 2. the above uses the predefined field of complex numbers CC, which has precision 53 bits. If you want a different precision, say 20 bits: sage: C.<i> = ComplexField(20) sage: A=matrix([[-1,-1+i],[1,0]]) sage: A.eigenvalues() [1.0000*I, -1.0000 - 1.0000*I] 3. or, if you prefer to work with exact quantities: sage: K.<i> = QuadraticField(-1) sage: A=matrix([[-1,-1+i],[1,0]]) sage: A.eigenvalues() [i, -i - 1] Hope this helps, Alex On Fri, Nov 7, 2008 at 3:21 PM, DJDANG <[EMAIL PROTECTED]> wrote: > > Hi everyone, I'm having this problem finding the correct eigenvalues > of a matrix. I've tried the code with other problems and worked, but > It doesn't work with this one. The exercise is this one: > > -Find the eigenvalues and eigenvectors of the matrix > A=(matrix[[-1,-1+i],[1,0]]) > > When I do this problem on a paper the result shows both lambdas as > lambda1=i and lambda2=-1-i; but when I try to do it in sage, it throws > me this: labmda1=-(sqrt(4i-3)-1)/2 and lambda2=(sqrt(4i-3)-1)/2. > > I think it might be an equality in the results but i havent been able > to prove it. > If anybody can help me to find a way to solve this problem showing the > lambdas I get when doing it on paper in sage, I'd be thankfull > > Thanks in advance, > Daniel > > > -- Alex Ghitza -- Lecturer in Mathematics -- The University of Melbourne -- Australia -- http://www.ms.unimelb.edu.au/~aghitza/<http://www.ms.unimelb.edu.au/%7Eaghitza/> --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
