[R] r: eviews and r // eigen analysis

[Michael Grant]

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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