Finding SVD of Matrix H: Summing H1 and H2's SVD Values?

[EngWiPy]

Hi,

I need to find the singular value decomposition (SVD) of a matrix H=H1+H2. Is this equivalent to sum the SVD values of H1 and H2?

Thanks

 

[AlephZero]

No. For a counterexample, suppose H1 and H2 are both nonsingular but H1+H2 is singular.

All the singular values of H1 and H2 are positive, but at least one singular value of H1+H2 is zero.

 

[EngWiPy]

No. For a counterexample, suppose H1 and H2 are both nonsingular but H1+H2 is singular.

All the singular values of H1 and H2 are positive, but at least one singular value of H1+H2 is zero.

Ok. Thanks.