Greetings everyone!
I have a question concerning the (right) eigenvectors returned from (MKL) LAPACK's dgeev.
There is the dgeev example at
intels dgeev example
where the matrix
A = {{-1.01, 3.98, 3.30, 4.43, 7.31},
{ 0.86, 0.53, 8.26, 4.96, -6.43},
{-4.60, -7.04, -3.89, -7.66, -6.16},
{ 3.31, 5.29, 8.20, -7.33, 2.47},
{-4.81, 3.55, -1.51, 6.18, 5.58}};
is diagonalized. On my machine I can reproduce the results given in the link. Then, with more digits than provided in the example, the first eigenvalue and -vector (lambda, v) read (in Mathematica notation, "I" is the imaginary unit)
lambda = 2.858133 + 10.762750 I;
v = {0.108065 + 0.168648 I,
0.406313 - 0.259010 I,
0.102358 - 0.508802 I,
0.398631 - 0.091333 I,
0.539535 + 0.000000 I};
When I check in Mathematica if the eigenpair satisfies
A v = lambda v
(as it should, according to the documentation) it turns out that this is not the case :
in: A.v
out: { 4.441 + 11.539 I,
-5.131 + 13.895 I,
-5.630 - 19.365 I,
-3.115 + 6.718 I,
5.526 + 7.408 I };
in: lambda v
out: { -1.506 + 1.645 I,
-10.341 + 4.443 I,
-11.924 - 1.516 I,
-9.884 + 6.165 I,
1.542 + 5.806 I }
And indeed, the eigenvectors provided from Mathematica are different and they furthermore satisfy the eigenvalue equation as expected
in: {eval, evec} = Eigensystem;
in: A . evec[[1]]
out: { 3.225 - 0.344 I,
1.766 + 6.653 I,
-6.313 + 1.264 I,
0.933 + 3.021 I,
3.537 - 1.457 I}
in: eval[[1]] evec[[1]]
out: {3.225 - 0.344 I,
1.766 + 6.653 I,
-6.313 + 1.264 I,
0.933 + 3.021 I,
3.537 - 1.457 I}
Any idea where I am going wrong would be highly appreciated.
Have a nice day and thank you!
phys
