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Systems of linear equations

  1. Sep 19, 2007 #1
    1. The problem statement, all variables and given/known data
    A is an nxn symmetric and positive definate matrix. Show that A admits a factorization A=LU
    In other words, no zero pivot is encountered during the elimination process.

    2. Relevant equations
    cholesky factorization


    3. The attempt at a solution
    I think all I have to show is that after 1 step in G.E. a(1,1) does not equal 0 and that the first row is the same as the first row in A and the first column is all zeros except for a(1,1). then show that the remaining (n-1)x(n-1) matrix is symmetric and positive definate. I showed that a(1,1) is not zero but I don't know how to prove the (n-1)x(n-1) matrix is positive definate and symmetric.
    any help or suggestions?
     
    Last edited: Sep 19, 2007
  2. jcsd
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