eigenvector problem
- Subject: eigenvector problem
- From: Leo Butler
- Date: Tue, 10 Feb 2009 20:19:44 +0000 (GMT)
Hello,
I have encountered the following problem. I am unsure of its origins.
The charpoly of the 6x6 matrix is (x^3-3x-1)^2, so the eigenvector
problem can be solved symbolically (maple does it in < 1sec on my
work desktop).
Leo
<session>
Maxima 5.16.3 http://maxima.sourceforge.net
Using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (aka GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) A : matrix([0, 0, -1, 0, 0, 0], [2, 0, 0, 0, 1, 0], [-4, 0, 0, -1,
-1, 0], [0, -2, -1, 0, 0, -1], [1, 2, 0, 0, 0, 1], [-2, 1, 1, -2, 1,
0]);
[ 0 0 - 1 0 0 0 ]
[ ]
[ 2 0 0 0 1 0 ]
[ ]
[ - 4 0 0 - 1 - 1 0 ]
(%o1) [ ]
[ 0 - 2 - 1 0 0 - 1 ]
[ ]
[ 1 2 0 0 0 1 ]
[ ]
[ - 2 1 1 - 2 1 0 ]
(%i2) eigenvectors(A);
Maxima encountered a Lisp error:
Error in PROGN [or a callee]: Caught fatal error [memory may be
damaged]
Automatically continuing.
To reenable the Lisp debugger set *debugger-hook* to nil.
(%i3) eigenvalues(A);
- 3/2
sqrt(3) %i 1 3 sqrt(473) %i 1 1/3
(%o3) [[(- ---------- - -) (------------------- + -)
2 2 2 2
sqrt(3) %i 1
5 (---------- - -)
2 2 sqrt(3) %i 1
+ ------------------------------, (---------- - -)
- 3/2 2 2
3 sqrt(473) %i 1 1/3
3 (------------------- + -)
2 2
sqrt(3) %i 1
- 3/2 5 (- ---------- - -)
3 sqrt(473) %i 1 1/3 2 2
(------------------- + -) + ------------------------------,
2 2 - 3/2
3 sqrt(473) %i 1 1/3
3 (------------------- + -)
2 2
- 3/2
3 sqrt(473) %i 1 1/3 5
(------------------- + -) + ------------------------------], [2, 2,
2]]
2 2 - 3/2
3 sqrt(473) %i 1 1/3
3 (------------------- + -)
2 2
</session>
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