Cholesky Factorization Calculator
Factor a real symmetric positive-definite 2–5 dimensional matrix into a lower-triangular factor.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Validate symmetry and compute each lower-triangular entry from previously completed columns.
A=LLᵀ; Lii=√(Aii−ΣLik²)
Worked example
Matrix4,2;2,3 gives L=2,0;1,√2 and determinant8.
Assumptions and input details
Positive-definite well-conditioned matrices only; no pivoted semidefinite decomposition or matrix repair. Entry count must be a square and symmetry is checked with a scale-relative tolerance.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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