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Is SVD linear?

  1. Mar 18, 2012 #1
    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
     
  2. jcsd
  3. Mar 18, 2012 #2

    AlephZero

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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.
     
  4. Mar 18, 2012 #3
    Ok. Thanks.
     
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