# [Numpy-discussion] finding eigenvectors etc

devnew@gmai... devnew@gmai...
Wed Feb 20 01:08:17 CST 2008

```hi
i was calculating eigenvalues and eigenvectors for a covariancematrix
using numpy

evalues,evect=eigh(covarmat)

for a sample covarmat like
[[  1.69365981e+13 , -5.44960784e+12,  -9.00346400e+12 , -2.48352625e
+12]
[ -5.44960784e+12,   5.08860660e+12,  -8.67539205e+11  , 1.22854045e
+12]
[ -9.00346400e+12,  -8.67539205e+11,   1.78184943e+13  ,-7.94749110e
+12]
[ -2.48352625e+12 ,  1.22854045e+12,  -7.94749110e+12 ,  9.20247690e
+12]]

i get these
evalues
[  3.84433376e-03,  4.17099934e+12 , 1.71771364e+13 ,  2.76980401e+13]

evect
[[ 0.5        -0.04330262  0.60041892 -0.62259297]
[ 0.5        -0.78034307 -0.35933516  0.10928372]
[ 0.5         0.25371931  0.3700265   0.74074753]
[ 0.5         0.56992638 -0.61111026 -0.22743827]]

what bothers me is that for the same covarmat i get a different set of
eigenvectors and eigenvalues when i use java library Jama's methods
Matrix faceM = new Matrix(faces, nrfaces,length);
Matrix faceM_transpose = faceM.transpose();
Matrix covarM = faceM.times(faceM_transpose);
EigenvalueDecomposition E = covarM.eig();
double[] eigValue = diag(E.getD().getArray());
double[][] eigVector = E.getV().getArray();

here the eigValue=
[-6.835301757686207E-4, 4.170999335736721E12, 1.7177136443134865E13,
2.7698040117669414E13]

and eigVector
[
[0.5, -0.04330262221379265, 0.6004189175979487, 0.6225929700052174],
[0.5, -0.7803430730840767, -0.3593351608695496, -0.10928371540423852],
[0.49999999999999994, 0.2537193127299541, 0.370026504572483,
-0.7407475253159538],
[0.49999999999999994, 0.5699263825679145, -0.6111102613008821,
0.22743827071497524]
]

I am quite confused bythis difference in results ..the first element
in eigValue is different and also the signs in last column of
eigVectors are diff..can someone tell me why this happens?
thanks
dn

```