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
<mover@Domain.Removed<mailto:mover@Domain.Removed>> wrote:
Dear lapack team,
I tried to compute the lefteigenvector 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 lefteigenvector 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 lefteigenvector 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<mailto: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.
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