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### [Lapack] Possible bug in the computation of complex left eigenvectors

 ```Hi Sergio, The definition of a left eigenvector v associated with eigenvalue lambda for matrix A is v^H * A = v^H * lambda. (And v needs to be nonzero.) So if you take the left eigenvector v and associated eigenvalue lambda v = [-0.7071 * i; 0.7071]; lambda = i; for matrix A A=[[0,1]; [-1,0]] and you get: v^H * A = [ -0.7071; 0.7071i ]; v^H * i = [ -0.7071; 0.7071i ]; All good. Note: From April 2nd 2011 to August 9th 2012 (SVN), so for LAPACK versions 3.3.1, 3.4.0 and 3.4.1, the comment in the subroutines SGEEV, DGEEV, etc. were not correct and had a ^T instead of ^H for the definition left eigenvectors. Bug was introduced in 3.3.1 and removed in 3.4.2. Cheers, Julien. On Jan 5, 2014, at 3:02 AM, Sergio Mover > wrote: Dear lapack team, I tried to compute the left-eigenvector of the matrix A=[[0,1]; [-1,0]] using the function zgeev and I got some results that seem wrong. I get the eigenvalue eig=I and the associated left-eigenvector vect = [-0.7071 * I, 0.7071]. However, this is not a left eigenvector: vect * A = [-0.701, -0.701] eig * vect = [0.701, 0.701*I] The correct left-eigenvector for I should be [0.701, -0.701*I] Also the other eigenvalue, eigenvector pair that is returned by zgeev seems wrong (eig= -I, vect=[0.707*I, 0.707]) I bumped into this problem using the lapacke c interface, but I reproduced it also with fortran (I used the example code provided online for zgeev). I also tried the examples using the svn version of the library, but I get the same results. I attach a tar.gz archive with the source code and the test case to reproduce the issue. As I am new to lapack I could have missed some details and I could have misused the library. Thank you, Sergio Mover mover@Domain.Removed PS: I also tried to use the forum, but I cannot post the bug report since the website always mark it as spam. _______________________________________________ Lapack mailing list Lapack@Domain.Removed http://lists.eecs.utk.edu/mailman/listinfo/lapack -------------- next part -------------- An HTML attachment was scrubbed... URL: ```
 Current Thread [Lapack] Possible bug in the computation of complex left eigenvectors, Sergio Mover [Lapack] Possible bug in the computation of complex left eigenvectors, Langou, Julien <=

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