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

  • SchurDecomposition[ m ] yields the Schur decomposition for a numerical matrix m. The result is a list q , t where q is an orthogonal matrix and t is a block upper triangular matrix.
  • The original matrix m is equal to q . t . Conjugate[Transpose[ q ]].
  • SchurDecomposition[ m , Pivoting -> True] yields a list q , t , d where d is a permuted diagonal matrix such that m . d is equal to d . q . t . Conjugate[Transpose[ q ]].
  • See the Mathematica book: Section 3.7.10.
  • See also Implementation NotesA.9.44.27MainBookLinkOldButtonDataA.9.44.27.
  • See also: QRDecomposition, LUDecomposition, SingularValues, JordanDecomposition.
  • Related package: LinearAlgebra`Cholesky`.

    Further Examples

    This is the Schur decomposition of an inexact 3 x 3 matrix.

    In[1]:=

    Out[1]=