# Cholesky Decomposition of a Sparse Symmetric Positive Semidefinite (SPSD) Singular Matrix

**URL:** <https://discourse.julialang.org/t/cholesky-decomposition-of-a-sparse-symmetric-positive-semidefinite-spsd-singular-matrix/119682>\
**Category:** Numerics\
**Tags:** linearalgebra, numerics, sparse, factorization\
**Created:** [September 21, 2024, 2:57pm UTC](https://discourse.julialang.org/t/cholesky-decomposition-of-a-sparse-symmetric-positive-semidefinite-spsd-singular-matrix/119682 "2024-09-21T14:57:40Z")\
**Posts on this page:** 1\
**Showing post:** 3

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**Author:** ![RoyiAvital](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/royiavital/32/571_2.png) [@RoyiAvital](https://discourse.julialang.org/u/RoyiAvital)\
**Post date:** [September 22, 2024, 6:01am UTC](https://discourse.julialang.org/t/cholesky-decomposition-of-a-sparse-symmetric-positive-semidefinite-spsd-singular-matrix/119682/3 "2024-09-22T06:01:13Z")

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The context I encountered it is in [Solve Large Scale Underdetermined Linear Equation with per Element Equality Constraint](https://discourse.julialang.org/t/119655).

The matrix to decompose, \boldsymbol{B}\_{\mathcal{U}}, is SPSD. When I set `check = false` I get the correct result. Yet I wonder if the missing pivot is crucial in this context.

I thought it would be better in the original thread as it is the first that show up when you do a Google search. So it is better to have high Information / Thread ratio (The same problem for the 2 cases: Dense / Sparse).

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