Proof: inverse of a positive definite matrix is positive definite

Discussion in 'Math' started by qin841019, Jan 31, 2007.

  1. qin841019

    Thread Starter New Member

    Jan 31, 2007
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    0
    I am taking a course in numerical computing, it is very frustrating to me. Many of the problems are difficult to do and the book does not give enough explanation. Here I have a problme asking me to prove that "the inverse of a positive definite matrix is positive definite"

    I have tried this problem, the best i can do is to get the inverse of A:
    if A is positive definite, A = L*(transpose(L))
    then inverse(A) = (transpose(L))' * L'

    then what is the next step? maybe i was wrong in the first place? What's the approach to prove this problem?
    I am really stuck in this problem.
    Please help
     
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