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I am trying to calculate the Cholesky decomposition of a precision matrix. I was expecting a Lower triangular matrix $L$ where $L_{ii}>0$ for all $i$. However, the last element in the diagonal is almost equal to $0$ around $10^{-8}$. I am not sure why?

This is my precision matrix

$A=\pmatrix{2& -1& -1& 0\\ -1& 2& 0& -1\\ -1& 0& 2& -1\\ 0 &-1& -1& 2}$.

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Without saying what your matrix is, we can't help you. –  J. M. May 18 '12 at 3:44
    
Dimensions, singular values, what precision, etc, etc,... –  copper.hat May 18 '12 at 3:52
2  
Do you realize this is a singular matrix? $(1,1,1,1)^T$ is in the null space. –  copper.hat May 18 '12 at 4:46
    
@copper.hat: something's up for OP to keep trying to decompose singular matrices in his/her last few questions... I wonder. :) –  J. M. May 18 '12 at 6:33
    
@J.M.: He's lost in eigenspace... –  copper.hat May 18 '12 at 6:53
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