Mathematica 9 is now available
 Documentation / Mathematica / Built-in Functions / Lists and Matrices / Matrix Operations /
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=



    Any questions about topics on this page? Click here to get an individual response.Buy NowMore Information
    THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
    SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.