It been thirty years since I was emeshed in QM and lost in Hilbert space :O). So if I'm sloppy some-someone correct me. IN A NUTSHELL: Note one vector is the same in both sets (except for the sign). Necessarily, the four remaining vectors (degenerate BTW) in each set span the same subspace, i.e., form an orthonormal basis for that subspace. One should rotate into the other. It would be a nice exercise (really)to convince yourself of that, providing some feel, i.e., visualization, of what you are dealing with. Regards, Michael Grant
--- Clark Allan <Allan at STATS.uct.ac.za> wrote:
hi all i have a question that about the eigen analysis found in R and in eviews. i used the same data set in the two packages and found different answers. which is incorrect? the data is: aa ( a correlation matrix) 1 0.9801 0.9801 0.9801 0.9801 0.9801 1 0.9801 0.9801 0.9801 0.9801 0.9801 1 0.9801 0.9801 0.9801 0.9801 0.9801 1 0.9801 0.9801 0.9801 0.9801 0.9801 1 now
svd(aa)
$d
[1] 4.9204 0.0199 0.0199 0.0199 0.0199
$u
[,1] [,2] [,3]
[,4] [,5]
[1,] -0.4472136 9.283999e-18 1.939587e-17
-2.101554e-15 0.8944272
[2,] -0.4472136 8.089763e-01 7.115435e-17
3.091235e-01 -0.2236068
[3,] -0.4472136 2.178563e-02 8.226578e-18
-8.657513e-01 -0.2236068
[4,] -0.4472136 -4.153810e-01 -7.071068e-01
2.783139e-01 -0.2236068
[5,] -0.4472136 -4.153810e-01 7.071068e-01
2.783139e-01 -0.2236068
$v
[,1] [,2] [,3] [,4]
[,5]
[1,] -0.4472136 0.00000000 0.000000e+00 0.0000000
0.8944272
[2,] -0.4472136 0.80897632 -4.976488e-17 0.3091235
-0.2236068
[3,] -0.4472136 0.02178563 1.077421e-17 -0.8657513
-0.2236068
[4,] -0.4472136 -0.41538097 -7.071068e-01 0.2783139
-0.2236068
[5,] -0.4472136 -0.41538097 7.071068e-01 0.2783139
-0.2236068
the results from Eviews is:
eigenvectors = (note that Eviews arranges the eigen
vectors in ascending
order of the size of the eigen values)
0.305963 -0.266024 -0.219066 -0.766569 0.447214
0.315257 -0.603871 0.075772 0.574640 0.447214
0.461958 0.726861 0.199385 0.136062 0.447214
-0.482609 0.185567 -0.700705 0.204124 0.447214
-0.600569 -0.042534 0.644614 -0.148258 0.447214
eigen values =
0.019900
0.019900
0.019900
0.019900
4.920400
NOTE THAT THE EIGEN VALUES ARE THE SAME BUT THE
EIGEN VECTORS ARE NOT!!!
why is this so?
if one sets aa=
1.000000 0.500000 0.250000
0.500000 1.000000 0.350000
0.250000 0.350000 1.000000
then both packages give the same answers.>
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