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What is the normal procedure to verify that I got the correct results (eigenvalues and eigen vectors) from the eigenvalue problem?

I'm using the lapack library to solve eigenvalue problem summarized below. I've 2 matrices K and M and I get the negative results for eigenvalues which arouse my suspicion that the results could be wrong. In order to verify that, the given solutions (eigenvalues and eigenvectors) must comply with that K*X = λ*M*X equation where λ=eigenvalues and X =eigenvectors. I multiplied that λ*M, where I was expecting the K matrix but the results(named as "Verification phase" below) are not even close to those inner products of K matrix.

What am I doing wrong here ?

K MATRIX

0.2400 0.3900 0.4200 -0.1600

0.3900 -0.1100 0.7900 0.6300

0.4200 0.7900 -0.2500 0.4800

-0.1600 0.6300 0.4800 -0.0300

M MATRIX

4.1600 -3.1200 0.5600 -0.1000

-3.1200 5.0300 -0.8300 1.0900

0.5600 -0.8300 0.7600 0.3400

-0.1000 1.0900 0.3400 1.1800

EIGENVECTORS ARE:

-0.6901E-01 0.3080E+00 -0.4469E+00 -0.5528E+00

-0.5740E+00 0.5329E+00 -0.3708E-01 -0.6766E+00

-0.1543E+01 -0.3496E+00 0.5048E-01 -0.9276E+00

0.1400E+01 -0.6211E+00 0.4743E+00 0.2510E+00

EIGENVALUES

-2.2254 -0.4548 0.1001 1.1270

VERIFICATION PHASE (λ*M )

-9.2579 6.9434 -1.2463 0.2225

1.4188 -2.2874 0.3774 -0.4957

0.0560 -0.0831 0.0761 0.0340

-0.1127 1.2285 0.3832 1.3299

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# Verification sequence of eigenvalue problem

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