Cholesky decomposition - positive values requirement

May 2010
1
0
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'?
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
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 \(\displaystyle A\) is a symmetric positive definite matrix, then \(\displaystyle A\) can be factored into a product \(\displaystyle LL^T\), where \(\displaystyle L\) is lower triangular with positive diagonal elements.