I wrote some code to solve the general eigenvalue problem and now I am comparing my results agains LAPACK, DSPGVX function. I just worked with this example.

So I obtained the 4 auto vectors

{

{-0.0319133, -0.265466, -0.713483, 0.64765},

{-0.425628, -0.520961, -0.714215, 0.193227},

{0.32702, 0.565845, -0.37129, -0.659561},

{-0.682699, -0.056645, 0.0771025, 0.724409}

}

and auto values

{-2.22545, 1.12704, -0.454756, 0.100076}

both with my code and with Mathematica and results agree.

But in the previous link, auto vectors reported from LAPACK are completely different.

Eigenvalues

-0.4548 0.1001

Selected eigenvectors

1 2

1 0.3080 0.4469

2 0.5329 0.0371

3 -0.3496 -0.0505

4 -0.6211 -0.4743

Whom should I trust?

P.S. I also checked that my auto values/autovectors are correct since they yield A*x-lambda*B*x=0, while the values from LAPACK do not.