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Matrix inequality

  1. Jan 20, 2012 #1
    I am puzzled about this simple case,

    Suppose we have (A+B)T(A+B) <= (A+B1)T(A+B1),

    Can we say something about the relation between BTB and B1TB1?

    For example, is it correct if I say BTB <= B1TB1?
  2. jcsd
  3. Jan 20, 2012 #2


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    Science Advisor
    Gold Member

    Expand all the terms on each side. You'll see that
    [tex]A^T A[/tex]
    cancels, leaving three additional terms on each side. Does your hypothesis follow?
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