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Math Help - Cholesky decomposition - positive values requirement

  1. #1
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    Cholesky decomposition - positive values requirement

    I want the G matrix (cholesky decomposition) in

    A =GG'

    to be of positive numbers only. A is a positive (all elements) symmetric matrix.
    Is there a theorem that says 'if all the elements in A is positive, so is G'?
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  2. #2
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    Quote Originally Posted by ivarkol View Post
    I want the G matrix (cholesky decomposition) in

    A =GG'

    to be of positive numbers only. A is a positive (all elements) symmetric matrix.
    Is there a theorem that says 'if all the elements in A is positive, so is G'?
    Property 6 in book says:
    If A is a symmetric positive definite matrix, then A can be factored into a product LL^T, where L is lower triangular with positive diagonal elements.
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