A Hessenberg decomposition is a matrix decomposition of a matrix
into a unitary matrix and a Hessenberg matrix
such that
where
denotes the conjugate transpose .
Hessenberg decomposition is implemented in the Wolfram
Language as HessenbergDecomposition [m ].
Hessenberg decomposition is the first step in Schur decomposition . Hessenberg decomposition on an matrix requires arithmetic operations.
See also Hessenberg Matrix ,
Matrix
Decomposition ,
Schur Decomposition
Explore with Wolfram|Alpha
References Golub, G. H. and Van Loan, C. F. "The Hessenberg and Real Schur Forms." §7.4 in Matrix
Computations, 3rd ed. Baltimore, MD: Johns Hopkins University Press, pp. 361-372,
1996.
Cite this as:
Weisstein, Eric W. "Hessenberg Decomposition."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/HessenbergDecomposition.html
Subject classifications