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THE FEUTEX TOOLKIT

2×2 Cholesky Factorization

Factor a symmetric positive-definite matrix into a lower triangular matrix and its transpose.

Math workspace● Runs in your browser
01 Your input
02 Your result
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FormulaL11 = sqrt(a); L21 = b/sqrt(a); L22 = sqrt(d-b**2/a)
Sources and model references

Made for real tasks

  • Factor a symmetric positive-definite matrix into a lower triangular matrix and its transpose.
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Worked example

Inputs

Top-left entry
4 number
Off-diagonal entry
2 number
Bottom-right entry
3 number

Expected results

L11
2 number
L21
1 number
L22
1.414213562 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter top-left entry, off-diagonal entry, bottom-right entry.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "a": 4,
  "b": 2,
  "d": 3
}

Accuracy and scope

Symmetric matrix [[a,b],[b,d]]. Returns L with A=L*transpose(L).

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.