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 9, 2005 #1
    Use the [itex] LDL^T [/itex] factorization to solve the following linear system
    [tex] \left(\begin{array}{cccc|1}4&1&-1&0&7\\1&3&-1&0&8\\-1&-1&5&2&-4\\0&0&2&4&6\end{array}\right)[/tex]
    now i know ihow to get a matrix in the form LDL^T. But i was wondering how one would go about solving from there?

    Please help!
    Last edited: Nov 9, 2005
  2. jcsd
  3. Nov 10, 2005 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    That should be straight forward- the Cholesky decomposition is supposed to be the hard part! L here is a lower triangular matrix, LT is upper triangular, and D is diagonal, so going from LDLTX= A to DLTX= B is just a matter of "back substitution", starting from the value you get immediately in the last row and working up.
    Since D is diagonal, going from DLTX= B to LTX= C is just dividing by the diagonal elements. Finally, since LT is upper triangular, going from LTX= C to X= D is again back substitution, this time working from the top row down.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Linear Algebra question