Use this mathematical tool to inspect or reproduce the stated operation with inputs that satisfy its dimensional and domain requirements.

Matrix

Required list. A non-empty square matrix.

The cited overview of Matrix (mathematics) supplies background for the terminology and domain context used by this tool.^[1]

Factor a square matrix as P·A = L·U using Doolittle elimination with partial pivoting. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

L

Returned list. Unit lower-triangular factor.

U

Returned list. Upper-triangular factor.

Permutation

Returned list. Original row indices in pivoted order, so that P·A equals L·U.

• Floating-point rounding, ill-conditioned inputs, singular cases, tolerance choices, and rapidly growing output sets can affect numerical accuracy or feasibility.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

Check the result analytically on a small case and use an established numerical or symbolic library with suitable precision and diagnostics for consequential work.

• Matrix Determinant Calculator

  Compute the determinant of a square matrix by Gaussian elimination with partial pivoting.

• Matrix Inverse Calculator

  Invert a square matrix with Gauss-Jordan elimination under partial pivoting.

• Matrix Rank Calculator

  Count the pivots surviving Gaussian elimination with partial pivoting and a 1e-10 tolerance.