MATLAB Function Reference

hess

Hessenberg form of a matrix

Syntax

[P,H] = hess(A)
H = hess(A)

Description

H = hess(A) finds H, the Hessenberg form of matrix A.

[P,H] = hess(A) produces a Hessenberg matrix H and a unitary matrix P so that A = P*H*P' and P'*P = eye(size(A)).

Definition

A Hessenberg matrix is zero below the first subdiagonal. If the matrix is symmetric or Hermitian, the form is tridiagonal. This matrix has the same eigenvalues as the original, but less computation is needed to reveal them.

Examples

H is a 3-by-3 eigenvalue test matrix:

H =
   -149    -50   -154
    537    180    546
    -27     -9    -25

Its Hessenberg form introduces a single zero in the (3,1) position:

hess(H) =
   -149.0000    42.2037   -156.3165
   -537.6783   152.5511   -554.9272
           0     0.0728      2.4489

Algorithm

hess uses LAPACK routines to compute the Hessenberg form of a matrix:

Matrix A	Routine
Real symmetric	DSYTRD DSYTRD, DORGTR, (with output P)
Real nonsymmetric	DGEHRD DGEHRD, DORGHR (with output P)
Complex Hermitian	ZHETRD ZHETRD, ZUNGTR (with output P)
Complex non-Hermitian	ZGEHRD ZGEHRD, ZUNGHR (with output P)

See Also

eig, qz, schur

References

[1]  Anderson, E., Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK User's Guide, Third Edition, SIAM, Philadelphia, 1999.

helpwin

hex2dec