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Homework Help: Linear Algebra question

  1. Nov 16, 2005 #1
    ok question is to find the Cholesky Decomposition of this matrix

    [tex] \left(\begin{array}{ccc}2&-1&0\\-1&2&-1\\0&-1&2\end{array} \right) [/tex]

    now for the cholesky decomposition L i know how to find the first column that is
    [tex] \left(\begin{array}{ccc}\sqrt{2}&0&0\\-\frac{1}{\sqrt{2}}&\frac{3}{2}&?\\0&?&?\end{array}\right) [/tex]

    the qeustion marks mean that parts i cant figure out

    can someone please lhelp me !

    thank you
     
  2. jcsd
  3. Nov 16, 2005 #2

    CarlB

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    Gosh, it seems like you're on the right direction. Why don't you put A, B, and C into those question marks, take the transpose, multiply the two matrices and see what equations you get on A, B and C?

    Carl
     
  4. Nov 16, 2005 #3
    isn't there a more direct approach that doesn't involve matrix multiplication?

    like how i got the 3/ in the a22 position was as follows

    [tex] \sqrt{2 - \frac{1}{2}} [/tex]
    but how would ig oabout findin the ? in the a32 postiion??

    is it [tex] \frac{-1-0}{\frac{3}{2}} [/tex]
    is that correct??
     
  5. Nov 17, 2005 #4

    CarlB

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    Last edited: Nov 17, 2005
  6. Nov 21, 2005 #5
    i dont want to do it the wikipedia way its too hard i think. How would you do this question??

    PLease i need to figure this out !
     
  7. Nov 22, 2005 #6
    any help... anyone? i know that im not suppsoed to bump liek this but how would one go about doing this decomposition?

    For that matter, how would do the LDL transpose factorization for a matrix

    one method suggested to me was to reduce the origina lamtrix to the elementary matrix, and apply each of the row operatorions to a differnet elementary matrix and then finally mulitply them all so give the Lower triangular matrix

    but how would one go about fdind the D matrix?
     
  8. Nov 27, 2005 #7

    CarlB

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    The matrix multiplication for this problem should be fairly easy. That's what I would do.

    You're only going to end up with three equations in three unknowns. They will be quadratic in the unknowns, but you should be able to solve them without a lot of trouble.

    Carl

    Oh, and by the way, my Seahawks just one in overtime, improving their record to 9-2-0 continuing a win streak now at 7 games.
     
    Last edited: Nov 27, 2005
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