Thread: 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'?

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 is a symmetric positive definite matrix, then can be factored into a product , where is lower triangular with positive diagonal elements.