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

Matrix

Required list. Square matrix given as rows of equal length.

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

Householder QR decomposition of a square matrix: orthogonal Q and upper-triangular R with A = Q·R. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Q

Returned list. Orthogonal factor Q (Q·R reproduces the input).

R

Returned list. Upper-triangular factor R.

• 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.

• Cholesky Decomposition Calculator

  Factor a symmetric positive-definite matrix into a lower-triangular L where L times its transpose equals the input.

• LU Decomposition Calculator

  Factor a square matrix as P·A = L·U using Doolittle elimination with partial pivoting.

• Matrix Determinant Calculator

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