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LLT-Factorization help

  1. Feb 11, 2007 #1
    1. The problem statement, all variables and given/known data
    Determine directly the LLT-Factorization, in which L is a lower triangular matrix with positive diagonal elements, for the matrix

    | 4 1/2 1 |
    | 1/2 17/16 1/4 |
    | 1 1/4 33/64|

    2. Relevant equations
    I don't know.

    3. The attempt at a solution
    I don't know what to do; please help!

  2. jcsd
  3. Feb 12, 2007 #2


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    Science Advisor
    Homework Helper

    You mean LLT, where LT is the transpose of L? This is easy, why don't you just do it? Let L be an arbitrary lower triangular matrix, and compute the entries of LLT in terms of the entries of L. Then equate them with the corresponding entries in the matrix you're given to work with, and solve the equations. For example, if you had a 1x1 matrix (7), and were asked to find the LLT factorization, you let L = (a) be an arbitrary lower triangular matrix. Then you can compute the entries of LLT in terms of the entries of L: LLT = (a)(a) = (a2). Then you equate entries of this matrix with the entries of the matrix you're working with, (7). So you get a2 = 7. So a is either the postive or negative square root of 7, but since we have the condition "L has positive elements on its diagonal" we know a to be the positive root of 7. Your problem is similar, it's just that you'll get 3 + 2 + 1 = 6 equations instead of just 1 equation.
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