4

I don't understand why L must have strictly positive diagonal entries in Cholesky decomposition?:

$A = L*L^{T}$

Shrike Danny
  • 43
  • The solution is not unique if this is not required. – Hans Engler May 09 '19 at 17:34
  • You could simply let $S=-L$ and have $A=SS^{T}$, but the resulting factorization wouldn’t be a Cholesky factorization. This element of the definition of the Cholesky factorization makes the factorization unique. – Brian Borchers May 09 '19 at 17:35
  • Aside from the fact that $L_{j,j} = \sqrt{ A_{j,j} - \sum_{k=1}^{j-1} L_{j,k}^{2} } $? –  May 09 '19 at 18:00
  • @HansEngler, your comment as a one line answer would be the easiest complete solution. The only thing I would add is a reference that says as much. – Damien Jul 05 '23 at 22:33

0 Answers0