TOPICS
Search

Hessenberg Decomposition

A Hessenberg decomposition is a matrix decomposition of a matrix A into a unitary matrix P and a Hessenberg matrix H such that

PHP^(H)=A,

where P^(H) 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 n×n matrix requires 14n^3/3 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