This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Documentation / Mathematica / Built-in Functions / Lists and Matrices / Matrix Operations /


FilledSmallSquare QRDecomposition[m] yields the QR decomposition for a numerical matrix m. The result is a list q, r, where q is an orthogonal matrix and r is an upper triangular matrix.

FilledSmallSquare The original matrix m is equal to Conjugate[Transpose[q]] . r.

FilledSmallSquare For non-square matrices, q is row orthonormal.

FilledSmallSquare The matrix r has zeros for all entries below the leading diagonal.

FilledSmallSquare QRDecomposition[m, Pivoting -> True] yields a list q, r, p where p is a permutation matrix such that m . p is equal to Conjugate[Transpose[q]] . r.

FilledSmallSquare See Section 3.7.10.

FilledSmallSquare Implementation Notes: see Section A.9.4.

FilledSmallSquare See also: SchurDecomposition, LUDecomposition, SingularValueDecomposition, JordanDecomposition, CholeskyDecomposition.

FilledSmallSquare Related package: LinearAlgebra`Orthogonalization`.

FilledSmallSquare New in Version 2.

Further Examples