Question

I used the matlab functions svd() and eig() to decompose a positive
hermitian symmetric matrix R,

[Q, A] = eig(R);
[U, D, V] = svd(R);

then R is decomposed as,
R = Q A Q' (1)
Also
R = U D V' (2)

To calculate the signular vectors of V, is equivalent to calculate the
eigenvectors of R'R and similarly to calculate U, is equivalent ot
calculate the eigenvectors of RR'. Am I right?

My problem is
for the same eigen/singular value, sometimes there is a sign
difference for eigenvector (eu) and sigular vector(sv), why shouldn't
they be the same? How matlab implement svd()?

Thanks.

Answer 1

AV_i = lamda_i * U_i, either both U and V positive or negative is acceptable therefore the sign will change. solved.