# Thread: Cholesky decomposition - positive values requirement

1. ## 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'?

2. Originally Posted by ivarkol
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.