Schur decomposition

If A is a complex square matrixMathworldPlanetmath of order n (i.e. AMatn(C)), then there exists a unitary matrixMathworldPlanetmath QMatn() such that


where H is the conjugate transposeMathworldPlanetmath, D=diag(λ1,,λn) (the λi are eigenvaluesMathworldPlanetmathPlanetmathPlanetmathPlanetmath of A), and NMatn() is strictly upper triangular matrixMathworldPlanetmath. Furthermore, Q can be chosen such that the eigenvalues λi appear in any order along the diagonal. [GVL]


  • GVL Golub, H. Gene, Van Loan F. Charles: Matrix Computations (Third Edition). The Johns Hopkins University Press, London, 1996.
Title Schur decompositionMathworldPlanetmath
Canonical name SchurDecomposition
Date of creation 2013-03-22 13:42:12
Last modified on 2013-03-22 13:42:12
Owner Daume (40)
Last modified by Daume (40)
Numerical id 8
Author Daume (40)
Entry type Theorem
Classification msc 15-00
Related topic AnExampleForSchurDecomposition
Related topic ProofThatDetEAEoperatornametrA