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Singular value

  1. May 25, 2012 #1
    Is it true if I state:

    σmax(A-B) <= σmax(A) - σmin(B) ?

    I verify numerically that it is correct but how to prove it?
     
  2. jcsd
  3. May 25, 2012 #2

    HallsofIvy

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    If [itex]a\in A[/itex] then [itex]a\le max(A)[/itex]
    If [itex]b\in B[/itex] then [itex]b\ge min(a)[/itex] so [itex]-b\ge -min(B)[/itex]

    Adding, [itex]a-b\le max(A)- min(B)[/itex] for all a in A, b in B/
     
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