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Homework Help: Need help on understanding this notation

  1. Feb 21, 2010 #1
    20uqt11.jpg


    Where it says maxQ I don't understand.

    Q is a matrix, so are A and P.

    I know what q1 and the 2-norm of P are, but what on earth does max Q mean?

    I started with the matrix A, I've selected Q as positive definite arbitrarily, and I recieved a matrix P. I need to now find rho but I'm stuck on what max Q means.
     
  2. jcsd
  3. Feb 21, 2010 #2
    maxQ means to take the maximum over all possible Q that satisfy the given equation. q1 and P will vary depending on what the matrix Q is.
     
  4. Feb 22, 2010 #3
    I still really don't understand this part, can you simplify it a bit?

    Say if I have a matrix Q = [1 2; 3 4]

    What is the max Q?
     
  5. Feb 22, 2010 #4

    HallsofIvy

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    Science Advisor

    There is no such thing. Matrices are not "ordered" and so do not have "max" or "min".

    It's not "max Q", it is [tex]\begin{array} amax \\ Q\end{array}[/tex], the maximum taken by a numerical expression over all possible values of Q. This isn't saying anything about a maximum of Q, it's talking about the maximum value of the numerical expression [itex]q_1/||P||[/itex] where Q can be any matrix and P must be such that [itex]A^TP+ PA+ Q= 0[/itex]
     
  6. Feb 22, 2010 #5
    Ok thanks, so I don't need to alter the calculation of [itex]q_1/(2||P||)[/itex] and treat it the same as if [tex]\begin{array} amax \\ Q\end{array}[/tex] wasn't there?
     
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