Re: How can I compute eigenvectors?
- From: see.sig@xxxxxxxx (Victor Eijkhout)
- Date: Sat, 14 May 2005 10:24:38 -0400
Jeremy Watts <jwatts1970@xxxxxxxxxxx> wrote:
> "Murat Aykut" <murat_aykut@xxxxxxxxx> wrote in message
> news:1115995167.751620.305730@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> >I am a Computer Engineering student. And, on my project I must do PCA
> > training. So, I have computed eigenvalues via QR algorithm.
If you're doing PCA, your matrix is probably rectangular, not? In that
case you're doing singular values, not eigenvalues.
> I too have recently written a computer program that finds eigenvalues via
> the QR algorithm. As you know the QR algorithm effectively produces a Schur
> decomposition such that a general matrix 'A' can be written A = UTU* where
> 'U' is a unitary matrix and 'T' is upper triangular and '*' represents the
> conjugate transpose.
For rectangular A that becase UTV', where the size of T is the rank of
A.
> With each iteration of the QR algorithm we generate a 'Q matrix' and an 'R
> matrix' and from these form the matrix product 'RQ' which is then further
> QR decomposed and so on.
And that's where my knowledge ends. I can imagine that this doesn't work
for rectangular matrices.
V.
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- How can I compute eigenvectors?
- From: Murat Aykut
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- From: Jeremy Watts
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