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While I'm sure the complex eigenvalues of a transformation matrix are very interesting, I've never ran across a use for them in my work. They seem to have meaning in a universe where complex values for coordinates are possible. That universe would have three "space-like" and three "time-like" dimensions. I have enough problems with the on-rush of one dimension of time. Dale Tronrud. On 9/22/2014 10:40 AM, Chen Zhao wrote: > Hi Dale, > > Thank you for your reply! Yes, the real term of all eigenvalues are > very close to 1, and as I said in the previous email they matches a > 2-fold rotational matrix. But I am just curious, would you mind if > you give me a little bit of hint on what the imaginary space > represent? > > Thank you so much, Chen > > On Mon, Sep 22, 2014 at 1:26 PM, Dale Tronrud > <de...@daletronrud.com <mailto:de...@daletronrud.com>> wrote: > > > On 9/22/2014 10:10 AM, Chen Zhao wrote: >> Hi all, > >> I have a follow-up question here. I calculated the eigenvalues >> and the eigenvectors and some of them have imaginary terms. The >> real terms of the eigenvalues match a 2-fold rotation, but I am >> just wondering what the imaginary terms represent. It's been >> quite a while since I studied linear algebra. > > > The eigenvalues for a rotation matrix will have one that is real > and the other two complex. The eigenvector that corresponds to > the real value is the rotation axis. The other two are not useful > for your purpose. > > By the way, that real eigenvalue has better be equal to one! > > Dale Tronrud > >> Thank you so much, Chen > >> On Mon, Sep 22, 2014 at 10:41 AM, Philip Kiser <p...@case.edu >> <mailto:p...@case.edu> <mailto:p...@case.edu >> <mailto:p...@case.edu>>> wrote: > >> Cool. Glad to help. > >> On Mon, Sep 22, 2014 at 10:34 AM, Chen Zhao <c.z...@yale.edu >> <mailto:c.z...@yale.edu> <mailto:c.z...@yale.edu >> <mailto:c.z...@yale.edu>>> wrote: > >> Dear Philip, > >> Please forgive me! Yes it is eigenvectors that I am looking for. >> I was deriving myself and came to the conclusion that >> R=A^(-1)R'A, but I just forgot it is eigenvectors, and I forgot >> what the eigenvector is originally for. Thank you so much! > >> Sincerely, Chen > >> On Mon, Sep 22, 2014 at 10:22 AM, Philip Kiser <p...@case.edu >> <mailto:p...@case.edu> <mailto:p...@case.edu >> <mailto:p...@case.edu>>> wrote: > >> Hi Chen, > >> Wouldn't the fold of the NCS be clear from the PDB file? You >> could use superpose to superimpose one monomer onto the next >> member of the NCS group, and then take the rotation matrix output >> from that program to calculate the eigenvectors for the >> transformation. The NCS axis is parallel to one of those >> eigenvectors. > >> Philip > >> Philip > >> On Mon, Sep 22, 2014 at 10:13 AM, Chen Zhao <c.z...@yale.edu >> <mailto:c.z...@yale.edu> <mailto:c.z...@yale.edu >> <mailto:c.z...@yale.edu>>> wrote: > >> Dear all, > >> Is there a software that can print out the position and the fold >> of a NCS rotational axis from a PDB file? (just something like >> molrep self-rotation on a reflection file) I cannot use molrep >> because the RMSD between the two copies are too high, and I just >> want to cut a certain region for calculation. I don't know >> whether calculated Fc from the truncated PDB works in molrep >> self-RF, but I am thinking whether there is a more >> straightforward way. > >> Thanks a lot in advance! > >> Sincerely, Chen > > > > > > > -----BEGIN PGP SIGNATURE----- Version: GnuPG v2.0.22 (MingW32) iEYEARECAAYFAlQgkB8ACgkQU5C0gGfAG130YACdHjpeAi7AMKP3jHmF5n7F4eGh i9oAoJEvpLZgBJMfypgu85B80cJ/zpNT =9CJD -----END PGP SIGNATURE-----
