Hello,
My understaing is that the relationship between eigenvalues () > 0, and singular values () is the following one:
Where;
are the singular values of a matrix X, size(X)=MxN
are the eigenvalues of the square matrix X'X (where ' is the complex conj transpose)
In my case, I have a matrix size(X)=1000×5
its singular values
sv=svd(X)
are
196942.326781670
30136.1778043317
23562.4701314061
5.85220605708913e-10
2.64092030198871e-12
wherease the square root of the eigenvalues of the matrix X'X
eigenvalues_sqrt=eig((X'*X)^.5)
are
196942.32678167
23562.470131406
30136.177804331
0.00120366636426888
0.00276213718421482
As you can see, the first 3 values are the same.
Here my question, why the last two are different since the eigenvalues are not < 0? is this because they are close to 0?
Any help would be highly appreciated!
Gabri
Best Answer