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

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SUMMARY

The discussion centers on the singular value decomposition (SVD) of a matrix H defined as the sum of two matrices H1 and H2. It is established that the singular values of H1 and H2 cannot simply be summed to obtain the singular values of H. A counterexample is provided where both H1 and H2 are nonsingular, yet their sum H1 + H2 results in a singular matrix, demonstrating that at least one singular value of H is zero despite all singular values of H1 and H2 being positive.

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EngWiPy
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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
 
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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.
 
AlephZero said:
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.
 

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