Posted by
Ferdinando M. Ametrano-3 on
URL: http://quantlib.414.s1.nabble.com/Using-quantlib-with-MS-VC-version-7-1-for-eigenvector-calcs-tp4693p4695.html
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