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Homework Help: Linear Algebra Notation

  1. Sep 12, 2010 #1
    I am having an issue with a problem, but mostly because I am confused by the notation. This is the question:

    If Q is an n x n symmetric matrix and e1, e2 (e is epsilon) are such that
    0 < e1*I </= Q </= e2*I

    show that

    1/e2 * I </= Q^-1 </= 1/e1 *I

    ( </= is less or equal to)



    My question is how can a matrix be compared with another matrix in a quantitative manner (less than, less or equal to, greater than, etc.) I am familiar with norms or determinants being compared that way since they are a scalar, but how would n x n matricies be compared this way? Any suggestions?

    Also I am assuming that the epsilons are scalar multipliers. The book I am using does not do a good job of clarifying this notation, but that is all I can imagine it would be.
     
  2. jcsd
  3. Sep 18, 2010 #2
    A<=B means that (B-A) is positive semi-definite. Of course this makes sense only when A, B are hermitian matrixes.
     
  4. Sep 18, 2010 #3

    Mark44

    Staff: Mentor

    On a side note, <= is widely understood to mean "less than or equal to" and >= is understood to mean "greater than or equal to."
     
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