I don't have time to track this down right now -- if no-one does it in
the next few days before I finish the current piece of work I will try to
find it myself.
R gets the wrong answer for the eigensystem of a (particular) 4x4
matrix (SunOS 4.1.4).
Running these commands:
x _ matrix(
c(-10, 0 ,0 ,0,
0 ,-0.3 ,0 ,0,
1 , 0.03 ,-0.594,0.0020,
1.2, 0.036,0.0792,-0.0176),byrow=T,ncol=4)
eigen(x)
R gives:
$values
[1] -10.2425681 -0.5515844 -0.3023825 0.1849350
$vectors
[,1] [,2] [,3] [,4]
[1,] -0.9881475178 0.06506841 -0.008135724 0.1387962
[2,] -0.0007232329 -0.07331061 0.993467182 0.0874528
[3,] 0.1014706558 0.95415639 0.046029849 0.2777959
[4,] 0.1151853550 -0.28280247 -0.104105822 0.9465290
S-PLUS 3.1 gives:
$values:
[1] -10.00000000 -0.59427468 -0.30000000 -0.01732532
$vectors:
[,1] [,2] [,3] [,4]
[1,] 1.0000000 0.00000000 0.0000000 0.000000000
[2,] 0.0000000 0.00000000 1.0000000 0.000000000
[3,] -0.1062897 -0.06249770 0.1009810 -0.003466636
[4,] -0.1193683 0.00858338 -0.1557992 -0.999560734
Note that the structure of the matrix actually gives us (-10.0) and (-0.3)
for free, so the S-PLUS answer looks right.
Even worse:
eigen(x[3:4,3:4])
gives (R)
$values
[1] -0.604684392 -0.006915608
$vectors
[,1] [,2]
[1,] 0.9910228 0.1336929
[2,] -0.1336929 0.9910228
(S-PLUS)
$values:
[1] -0.59427468 -0.01732532
$vectors:
[,1] [,2]
[1,] -0.06249770 -0.003466636
[2,] 0.00858338 -0.999560734
so it's not just some funky pivoting problem.
Or am I doing something *really* dumb?
Benjamin Bolker Dep't of Ecology and Evolutionary Biology,
ben@eno.princeton.edu Princeton University
tel: (609) 258-6886, fax: (609) 258-1334
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