<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Just to add a (hopefully, clarifying) comment. <div><br class="webkit-block-placeholder"></div><div>Hermitean matrix: eignevalues are real, eigenvectors are in in general complex</div><div>Real symmetric matrix: eigenvalues are real (because the matrix is Hermitean as well). The eigenvectors *CAN* be chose to be real. This does not imply that they *MUST* be chosen so. </div><div><br class="webkit-block-placeholder"></div><div>You may want to rethink to the previous replies in the light of this remark.</div><div>Also, I am almost certain that this very question has been already discussed in this forum. You may want to check the archive.</div><div><br class="webkit-block-placeholder"></div><div>Take care</div><div>Stefano B.</div><div><br><div><div>On Nov 19, 2007, at 12:03 PM, Paolo Giannozzi wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">On Nov 19, 2007, at 12:31 , Ion Errea wrote:</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div> <blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Does anyonone which are the reasons why you can get imaginary</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">displacements for phonon eigenmodes?</div> </blockquote><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">at q=0 both the dynamical matrix and its eigenvectors are real,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">but for a general q, the dynamical matrix is complex hermitian</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">and its eigenvectors are in general complex</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Paolo</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">---</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Paolo Giannozzi, Dept of Physics, University of Udine</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">via delle Scienze 208, 33100 Udine, Italy</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Phone +39-0432-558216, fax +39-0432-558222</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">_______________________________________________</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Pw_forum mailing list</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="mailto:Pw_forum@pwscf.org">Pw_forum@pwscf.org</a></div><div style="margin-top: 0px; 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margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; ">Stefano Baroni - SISSA</span></span></span></span></span></span></span></span></span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; 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margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; ">Please, if possible, don't</span></span></span></span></span></span></span></span></span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "> </span></span></span></span></span></span></span></span></span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; ">send me MS Word or PowerPoint attachments</span></span></span></span></span></span></span></span></span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; ">Why? See:</span></span></span></span></span></span></span></span></span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "><span class="Apple-style-span" style="font-size: 12px; "> </span></span></span></span></span></span></span></span></span></font><a href="http://www.gnu.org/philosophy/no-word-attachments.html"><font class="Apple-style-span" color="#0023E9" size="3"><span class="Apple-style-span" style="font-size: 12px;; color: rgb(0, 35, 233); -khtml-text-decorations-in-effect: underline; "><span class="Apple-style-span" style="color: rgb(0, 35, 233); font-size: 12px; -khtml-text-decorations-in-effect: underline; "><span class="Apple-style-span" style="color: rgb(0, 35, 233); font-size: 12px; -khtml-text-decorations-in-effect: underline; "><span class="Apple-style-span" style="color: rgb(0, 35, 233); font-size: 12px; -khtml-text-decorations-in-effect: underline; "><span class="Apple-style-span" style="color: rgb(0, 35, 233); font-size: 12px; -khtml-text-decorations-in-effect: underline; "><span class="Apple-style-span" style="color: rgb(0, 35, 233); font-size: 12px; -khtml-text-decorations-in-effect: underline; "><span class="Apple-style-span" style="color: rgb(0, 35, 233); font-size: 12px; -khtml-text-decorations-in-effect: underline; "><span class="Apple-style-span" style="color: rgb(0, 35, 233); font-size: 12px; -khtml-text-decorations-in-effect: underline; "><span class="Apple-style-span" style="color: rgb(0, 35, 233); font-size: 12px; -khtml-text-decorations-in-effect: underline; ">http://www.gnu.org/philosophy/no-word-attachments.html</span></span></span></span></span></span></span></span></span></font></a></div><div><br class="khtml-block-placeholder"></div><br class="Apple-interchange-newline"></span></span></span></span></span></span></span></span></span> </div><br></div></body></html>