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Derivation of Cholesky Decomposition

  1. Mar 13, 2016 #1
    1. The problem statement, all variables and given/known data
    Derive Cholesky Decomposition for a 3x3 matrix

    2. Relevant equations
    IN: S is Real matrix with dimensions 3x3 and is Symmetric and semi-definite
    Out: L is a Real matrix with dimensions 3x3 such that
    1. S=L*L^t
    2. L is lower-triangular

    3. The attempt at a solution
    We learned this in class, and here is what I have in my notes. Near the end, it starts not making sense, so I think I recorded something wrong, and I also don't fully get what's going on.

    upload_2016-3-13_18-6-41.png
     

    Attached Files:

  2. jcsd
  3. Mar 13, 2016 #2

    andrewkirk

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    You have miscopied the subscripts in the second last line. Replace ##L_{32}## by ##L_{33}##, ##L_{21}## by ##L_{22}## and ##L_{31}## by ##L_{32}## and then it will follow from the line above.
     
  4. Mar 13, 2016 #3
    Thank you so much! You're a life saver. This got me so confused. QR decomposition just clicked for me about 5 minutes ago, and now I get this too!
     
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