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Simple Linear Algebra question

  1. Feb 9, 2008 #1
    I have to do a LDL[tex]^{T}[/tex] transform of a symmetrical matrix:

    [2 -1 0]
    [-1 2 -1]
    [0 -1 2]

    And, I'm just wondering if I have to do a row exchange, or something. I can't remember if the L matrix has to have the form

    [x 0 0]
    [x x 0]
    [x x x]

    where the x's are nonzero numbers.

    Basically, I'm asking if that 0 in the lower left hand corner is all right, and if I only need to eliminate the -1 at positions 2,3 and 1,2

    Thank you.
  2. jcsd
  3. Feb 9, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, L is, by definition, a "Lower Triangular" matrix. It must have only 0s above ther diagonal. It is not required that all other numbers not be 0.
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