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Two-by-Two Cholesky Decomposition Calculator — result sheet
Factor a symmetric positive-definite two-by-two matrix into a lower triangular matrix and its transpose.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For [[a,b],[b,c]], L11=√a, L21=b/L11, L22=√(c−L21²).
The positive-definiteness checks are explicit before square roots are taken, preventing a misleading complex or undefined real result.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Diagonal entry a — minimum -1000000; maximum 1000000
- Off-diagonal entry b — minimum -1000000; maximum 1000000
- Diagonal entry c — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Diagonal entry a | 4 |
| Off-diagonal entry b | 2 |
| Diagonal entry c | 3 |
L=[[2,0],[1,1.4142]] for A=LLᵀ.
Assumptions and limits
- The matrix is real, symmetric, and intended for real-valued decomposition.
- a must be positive and ac−b² must be positive.
- Rounding is applied only by the display, not by the decomposition arithmetic.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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