Schur Decomposition

Author

Eric W. Weisstein
January 29, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/LinearAlgebra/SchurDecomposition.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/SchurDecomposition.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Example

(a=Table[Random[Integer,5],{3},{3}])//MatrixForm

Eigenvalues[a]

%//N

SchurDecomposition[a]

(SuperStar[Q])AQ = D+N

MatrixForm/@(s=SchurDecomposition[a//N])

Transpose[Conjugate[s[[1]]]].a.s[[1]]//Chop//MatrixForm

Q is unitary

Inverse[s[[1]]]-Transpose[Conjugate[s[[1]]]]//Chop//MatrixForm