Maths & numbers
Cholesky decomposition
Factor a small symmetric positive-definite matrix as L times its transpose.
A clear answer. Here’s how.
Computes a lower-triangular Cholesky factor for square matrices up to 6 × 6. Rejects asymmetry or non-positive pivots at tolerance 10⁻¹² × max(1, largest absolute input entry). The exported factor satisfies A≈L Lᵀ within floating-point error. Positive-semidefinite or near-singular inputs are not accepted; no automatic regularisation is applied.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Matrix: one row per line
4, 2 2, 3
Example result
| Factor | Row | C1 | C2 |
|---|---|---|---|
| L | 1 | 2 | 0 |
| L | 2 | 1 | 1.41421356237 |
A = L × transpose(L). Symmetry/positive-definiteness tolerance is 10⁻¹² × max(1, largest absolute input entry).