HessenbergDecomposition
gives the Hessenberg decomposition of a numerical matrix m.
Details and Options

- The result is given in the form {p,h} where p is a unitary matrix such that p.h.ConjugateTranspose[p]==m.
- The matrix m must be square.
Examples
open allclose allBasic Examples (1)
Scope (2)
Applications (1)
Properties & Relations (1)
Compute its Hessenberg decomposition:
The matrix is upper Hessenberg:
The original matrix is given by p.h.ConjugateTranspose[p]:
Possible Issues (1)
HessenbergDecomposition works only with matrices of approximate numerical values:

Use JordanDecomposition for exact matrices:
Text
Wolfram Research (2004), HessenbergDecomposition, Wolfram Language function, https://reference.wolfram.com/language/ref/HessenbergDecomposition.html.
CMS
Wolfram Language. 2004. "HessenbergDecomposition." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HessenbergDecomposition.html.
APA
Wolfram Language. (2004). HessenbergDecomposition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HessenbergDecomposition.html