Cholesky Decomposition Calculator
Result
L112
L211
L222
↗ Math
2×2 Cholesky Decomposition Calculator: scoped estimate with transparent input definitions.
Formula
L11=√a; L21=b/√a; L22=√(c−b²/a)
- Computes lower triangular factor for the real symmetric 2×2 positive definite matrix [[a,b],[b,c]]. Requires a>0 and c>b²/a. Not a general n×n decomposer. Formula: L11=√a; L21=b/√a; L22=√(c−b²/a).
- The main inputs are A11, A12 = A21, A22. Enter them in the units and format shown in the calculator.
- Keep comparable quantities in compatible units whenever the formula combines or compares them.
- Changing any input above recalculates the result with the same calculation engine used by this page.
Example: Cholesky Decomposition
Inputs
- A11: 4 positive
- A12 = A21: 2
- A22: 5
Given A11 (positive) = 4, A12 = A21 = 2, A22 = 5, primary result = 2.
Sample result: Calculating…
Frequently asked questions
What does the Cholesky Decomposition calculate?
2×2 Cholesky Decomposition Calculator: scoped estimate with transparent input definitions.
Which values should I enter?
Enter A11, A12 = A21, A22 using the units and format shown beside each field.
What formula does this calculator use?
The calculator uses the following relationship: L11=√a; L21=b/√a; L22=√(c−b²/a).
Why might my result differ from another source?
Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.
Does the result update automatically?
Yes. Changing an input updates the result using the same calculation engine shown on this page.