[Maxima-bugs] [ maxima-Bugs-3435971 ] eigenvectors produces wrong results

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Bugs item #3435971, was opened at 2011-11-10 00:02
Message generated for change (Settings changed) made by rtoy
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Category: Lisp Core - Solving equations
Group: None
>Status: Closed
Resolution: Invalid
Priority: 5
Private: No
Submitted By: https://www.google.com/accounts ()
Assigned to: Nobody/Anonymous (nobody)
Summary: eigenvectors produces wrong results

Initial Comment:
[vals,vec]:eigenvectors(matrix([0.2273,-0.0852],[-0.193,0.1794]));
rat: replaced -0.0164436 by -1134/68963 = -0.01644360019141
rat: replaced 0.1794 by 897/5000 = 0.1794
rat: replaced 0.2273 by 2273/10000 = 0.2273
rat: replaced -0.01644360019141 by -1091/66348 = -0.01644360040996
rat: replaced 0.1794 by 897/5000 = 0.1794
rat: replaced 0.2273 by 2273/10000 = 0.2273
rat: replaced 1.2057635497678905E-12 by 1/829350000000 = 1.2057635497678905E-12
rat: replaced 2.1637741760636258E+11 by 216377417606/1 = 2.16377417606E+11
rat: replaced 2.1637741760636258E+11 by 216377417606/1 = 2.16377417606E+11
(%o40) [[[0.07289999842889,0.33380000157111],[1,1]],[[[1,1.812206572769953]],[[1,
-1.25]]]]
However, the eigenvectors should be [0.62166748, -0.78328126] and [0.46864735,0.88338534].


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Comment By: Raymond Toy (rtoy)
Date: 2012-08-16 09:06

Message:
The eigenvalues computed by maxima are correct.

A : matrix([0.2273,-0.0852],[-0.193,0.1794]);

A . vec[1][1] - vals[1][1] * vec[1][1] -> matrix([0.0],[0.0])
A . vec[2][1] - vals[1][2] * vec[2][1] ->
matrix([-0.2609],[-.4728046948356808])

You were probably expecting the eigenvectors to be normalized to unit
length.  Eigenvectors are unique only up to a scale factor.

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