This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 QRDecomposition 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. The original matrix m is equal to Conjugate[Transpose[ q ]] . r. For non-square matrices, q is row orthonormal. The matrix r has zeros for all entries below the leading diagonal. 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. See the Mathematica book: Section 3.7.10. See also Implementation NotesA.9.44.27MainBookLinkOldButtonDataA.9.44.27. See also: SchurDecomposition, LUDecomposition, SingularValues, JordanDecomposition. Related package: LinearAlgebra`Cholesky`, LinearAlgebra`Orthogonalization`. Further Examples Performing a QRDecomposition on this x matrix yields a pair of matrices. In[1]:= Out[1]= This checks the result. In[2]:= Out[2]//MatrixForm=