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Homework Help: Cholesky Factorization Proofs

  1. Oct 15, 2011 #1
    1. The problem statement, all variables and given/known data
    Let A =[A11 A12; A*12 A22] be Hermitian Positive-definite.
    Use Cholesky factorizations
    A11 = L1L*1
    A22 = L2L*2
    A22-A*12 A-111 A12 = L3L*3

    to show the following:

    ||A22-A*12 A-111 A12||2≤||A||2

    2. Relevant equations

    3. The attempt at a solution

    Using the submultiplicative and triangle inequalities:

    ||A22||2+||A*12||2 ||A-111||2||A12||2≤||A||2
  2. jcsd
  3. Oct 18, 2011 #2
    Can anyone help?
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