Posted by
Elliffe, Eoin on
Apr 10, 2006; 8:47am
URL: http://quantlib.414.s1.nabble.com/Using-quantlib-with-MS-VC-version-7-1-for-eigenvector-calcs-tp4693p4694.html
What you say is certainly true, that is where V is the norm corr matrix.
V = W*diag(lambda)*W' even if the elements of W the eigenvector matrix
are negative.
I meant to say the eigenvalues are small and negative.
This is a problem....
-----Original Message-----
From:
[hidden email]
[mailto:
[hidden email]] On Behalf Of Ferdinando Ametrano
Sent: 07 April 2006 22:55
To: Elliffe, Eoin
Cc:
[hidden email]
Subject: Re: [Quantlib-users] Using quantlib with MS VC++ version 7.1
for eigenvector calcs
On 4/7/06, Elliffe, Eoin <
[hidden email]> wrote:
> I am using some algorithms from numerical recipes in C, namely tqli()
> and tridiag(), to calculate the eigenvectors/values of a corr matrix.
>
> I found that certain eigenvectors had elements with the correct
> magnitude but with opposite sign as those found using octave which
> uses hessenberg and schur decomposition.
why you consider this a problem?
Eigenvalues must be the same, eigenvector are defined with no regards to
their sign. If A is a matrix and k is one of its eigenvalue, there is an
eigenvector v of unit norm for which A v = k v holds.
The same equation holds also for -v, which is of unit norm too. So v
and -v are completely equivalent.
btw 4v, 7v, 2.3v are eigenvector too, even if their norm != 1
> I decided to take a look at Quantlib to see if I could remedy this.
glad you trust QuantLib... but it's not going to remedy a non-issue
hope it helps
ciao -- Nando
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