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Lower bound on det(A'DA) with A tall and D diagonal?

  1. Jan 20, 2013 #1
    Hi all,

    I searched all other threads but was unable to find something useful. Here is my question: I am looking for a lower bound on

    det(A'DA),

    where A is a MxN with M>=N (possibly tall and skiny) and D is diagonal, non-negative and of dimension M. In particular, I am looking for ways that separate the properties of the matrices A and D in this expression. I know that for M=N, we can rewrite it as

    (1) det(A'*D*A) = det(A)^2*det(D),

    which is very helpful. However, for the more general case with M>N, which is the one I am interested in, I am unable to derive a useful equality or lower bound (which would also be fine) that separates the matrices A and D in (1). Upper bounds are not useful in my particular application.

    Thanks a lot for your help,
    Wrukproek
     
  2. jcsd
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