Examples
Examples
Try the starting example
- Square real matrix, rows on separate lines
- 2,1 4,3
- Row permutation matrix P
- 0, 1; 1, 0
- Unit lower-triangular L
- 1, 0; 0.5, 1
- Upper-triangular U
- 4, 3; 0, -0.5
- Maximum reconstruction residual |P A − L U|
- 0
- Determinant from pivots
- 2
Try another scenario
- Square real matrix, rows on separate lines
- 4,3 6,3
- Row permutation matrix P
- 0, 1; 1, 0
- Unit lower-triangular L
- 1, 0; 0.666666666667, 1
- Upper-triangular U
- 6, 3; 0, 1
- Maximum reconstruction residual |P A − L U|
- 0
- Determinant from pivots
- -6
Calculation method
Calculation method
Row permutation matrix P
Partial row pivoting gives P such that P×A=L×U.
Unit lower-triangular L
Multipliers below the diagonal with unit diagonal entries.
Upper-triangular U
Eliminated upper-triangular factor.
Maximum reconstruction residual |P A − L U|
Maximum entrywise absolute difference using the original matrix and returned factors.
Determinant from pivots
Permutation parity × product of U diagonal entries.
Symbols and units
- a
- Square real matrix, rows on separate lines
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Partial-pivoted LU for real square matrices up to 20×20. A factorisation is not evidence that a matrix is well-conditioned or safely invertible. Double-precision results are approximate. Numeric tables use 12 significant digits and display components at roundoff scale (32 machine epsilons relative to their row or relevant calculation scale) as zero; scalar diagnostics retain full precision.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
ml-matrix: numerical decompositions ↗
Background reading; this does not imply endorsement or independent review of SumFizz.