Re: Multivariate pdf of a normal distribution

[Mike Miller]

On Sun, 6 Nov 2005, Henry F. Mollet wrote:

> octave:27> [E,L] = eig(ones(4))
> E =
>
>   -1.7253e-01    4.6929e-01    7.0711e-01    5.0000e-01
>   -1.7253e-01    4.6929e-01   -7.0711e-01    5.0000e-01
>   -4.9115e-01   -7.1328e-01   -6.8934e-17    5.0000e-01
>    8.3620e-01   -2.2530e-01    9.7203e-18    5.0000e-01
>
> L =
>
>  -0.00000   0.00000   0.00000   0.00000
>   0.00000  -0.00000   0.00000   0.00000
>   0.00000   0.00000  -0.00000   0.00000
>   0.00000   0.00000   0.00000   4.00000
>
> GNU Octave, version 2.1.71 (powerpc-apple-darwin8.1.0).
> Why do I not get the same results?

(Same results as below.)  Well, I don't really know, but we are both using 
Octave 2.1.71, though mine was compiled on Red Hat Linux with a different 
BLAS.  The ordering of the first three columns is arbitrary.  We have two 
columns that are the same to within machine precision.  The other two 
columns are more mysterious.  I'll have to guess that with zero 
eigenvalues, the eigenvectors are fairly arbitrary, so both solutions are 
correct but they've used slightly different algorithms.


> Only look at non-zero eigenvalue and corresponding eigenvector?

The problem is in identifying "non-zero" eigenvalues.  They usually are 
not *exactly* zero.

Mike

> > octave:6> [E,L] = eig(ones(4))
> > E =
> >
> >     -3.2026e-01    7.0711e-01    3.8397e-01    5.0000e-01
> >     -3.2026e-01   -7.0711e-01    3.8397e-01    5.0000e-01
> >     -2.2276e-01   -5.9234e-17   -8.3689e-01    5.0000e-01
> >      8.6328e-01   -4.4132e-19    6.8941e-02    5.0000e-01
> >
> > L =
> >
> >    -0.00000   0.00000   0.00000   0.00000
> >     0.00000   0.00000   0.00000   0.00000
> >     0.00000   0.00000   0.00000   0.00000
> >     0.00000   0.00000   0.00000   4.00000



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