Lu Decomposition Calculator
Result
2×2 LU Decomposition Calculator: scoped estimate with transparent input definitions.
Formula
- Doolittle LU without pivoting for a 2×2 matrix only. First pivot a11 must be nonzero; matrices needing row swaps are outside scope. Formula: L21=a21/a11; U22=a22−a21 a12/a11; L has unit diagonal.
- The main inputs are Matrix a11, Matrix a12, Matrix a21, Matrix 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: Lu Decomposition
- Matrix a11: 2 nonzero
- Matrix a12: 4
- Matrix a21: 6
- Matrix a22: 15
Given Matrix a11 (nonzero) = 2, Matrix a12 = 4, Matrix a21 = 6, Matrix a22 = 15, primary result = 2.
Sample result: Calculating…
Frequently asked questions
What does the Lu Decomposition calculate?
2×2 LU Decomposition Calculator: scoped estimate with transparent input definitions.
Which values should I enter?
Enter Matrix a11, Matrix a12, Matrix a21, Matrix a22 using the units and format shown beside each field.
What formula does this calculator use?
The calculator uses the following relationship: L21=a21/a11; U22=a22−a21 a12/a11; L has unit diagonal.
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.