1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: LDL factorization

  1. Dec 1, 2005 #1
    Find the [itex] LDL^T [/itex] factorization of this matrix

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

    now i can find the L matrix by gaussian elimination
    that yields
    [tex]L = \left(\begin{array}{ccc}{1&0&0\\\frac{-2}{3}&1&0\\0&\frac{-1}{2}&1\end{array}\right) [/tex]
    [tex] D = \left(\begin{array}{ccc}{\frac{1}{4}&0&0\\0&\frac{1}{3}&0\\0&0&\frac{1}{2}\end{array}\right) [/tex]

    i am pretty sure about the ansswer since i checked my working many times.
    However this is not the answer at the back of the book! In fact i am not even close!
    What am i doing wrong?? Can anyone please help me iwth this?
    Thank you for your help!
  2. jcsd
  3. Dec 1, 2005 #2


    User Avatar
    Science Advisor

    It's hard to tell what you did wrong when you did wrong when you don't tell us what you did! I did a quick "column reduction" to get L and didn't get any like you got.
  4. Dec 1, 2005 #3
    well i got those answers by Gaussian Elimination
    this is what i did

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

    R3 + 2R2
    [tex] \left(\begin{array}{ccc}{2&-1&0\\-2&3&0\\0&-1&2\end{array}\right) [/tex]

    [tex] \left(\begin{array}{ccc}{4&0&0\\-2&3&0\\0&-1&2\end{array}\right) [/tex]

    and my textbook says that that the D matrix is formed by dividing the square terms of the lower matrix formed and multiply that by the elementary matrix yielding
    [tex] D = \left(\begin{array}{ccc}{\frac{1}{4}&0&0\\0&\frac{ 1}{3}&0\\0&0&\frac{1}{2}\end{array}\right) [/tex]
  5. Dec 2, 2005 #4
    can anyone tell me what i have done wrong? my answer is not even close to the tedxxt book's answer. However all my steps with the row reductions are correct, as you can see.

    I was told that i was not supposed to use row reduction to get the lower matrix? SO what do i do then?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook