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Symmetric positive definite

  1. Feb 24, 2017 #1
    1. The problem statement, all variables and given/known data
    Here's the question :
    1x1+ 2x2 +0x3 + 0x4 = 1
    2x1+ 9x2 +1x3 + 0x4 = 6
    0x1+ 1x2 +9x3 + 4x4 = 2
    0x1+ 0x2 +4x3 + 3x4 = 8

    I' m asked to solve this question using Choelsky method ( We need the symmetric positive definite matrix when we are using this method)



    2. Relevant equations


    3. The attempt at a solution
    matrix A = $$\begin{bmatrix}
    1 & 2& 0 & 0 \\
    2 & 9 & 1 & 0 \\\
    0 & 1 & 9 & 4 \\
    0 & 0 & 4 & 3
    \end {bmatrix} $$


    the book stated that for the positive symmetric matrix , we need to ensure that max a_kj less than max a_ii ,
    But , in this example , i found that the a_44 which is 3 is less than a_43 which is 4 ... So , how could this be symmetric positive definite matrix ?
    How is it possible to solve using Choelsky method ?
     

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  3. Feb 24, 2017 #2

    BvU

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    The guy is called Cholesky.

    But it's clear what you are being asked, so go to work and see if and where it goes wrong !
     
  4. Feb 24, 2017 #3
    question solved
     
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