Martin Albrecht <[EMAIL PROTECTED]> writes:
> On Tuesday 14 October 2008, sonium wrote:
> > ((a, b, 0, 0),
> > (b,-a,b,0),
> > (0,b,a,b),
> > (0,0,b,-a))
>
> Hi, try this:
>
> sage: A.echelon_form() # row_reduction by constant entries only
> sage: A.echelon_form('frac') # over the fraction field
> sage: A.echelon_form('bareiss') # fraction free
I thought the original author wanted to find the diagonalised matrix? I.e.,
the eigenvalues on the diagonal. Did I misunderstand?
sage: A= matrix(SR,4,4,((a, b, 0, 0),(b,-a,b,0),(0,b,a,b),(0,0,b,-a)))
sage: A.parent()
Full MatrixSpace of 4 by 4 dense matrices over Symbolic Ring
sage: A.eigenvalues()
[-sqrt(sqrt(5)*b^2 + 3*b^2 + 2*a^2)/sqrt(2),
sqrt(sqrt(5)*b^2 + 3*b^2 + 2*a^2)/sqrt(2),
-sqrt(-sqrt(5)*b^2 + 3*b^2 + 2*a^2)/sqrt(2),
sqrt(-sqrt(5)*b^2 + 3*b^2 + 2*a^2)/sqrt(2)]
sage: A.jordan_form()
[-sqrt(2*x^2 + sqrt(5)*b^2 - 3*b^2)/sqrt(2)|
0| 0|
0]
[------------------------------------------+------------------------------------------+------------------------------------------+------------------------------------------]
[ 0| sqrt(2*x^2 + sqrt(5)*b^2 -
3*b^2)/sqrt(2)| 0|
0]
[------------------------------------------+------------------------------------------+------------------------------------------+------------------------------------------]
[ 0|
0|-sqrt(2*x^2 - sqrt(5)*b^2 - 3*b^2)/sqrt(2)|
0]
[------------------------------------------+------------------------------------------+------------------------------------------+------------------------------------------]
[ 0|
0| 0| sqrt(2*x^2 - sqrt(5)*b^2 -
3*b^2)/sqrt(2)]
Martin
--~--~---------~--~----~------------~-------~--~----~
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
-~----------~----~----~----~------~----~------~--~---
