1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Linear Algebra question
Loading...