hess

Hessenberg form

Calling Sequence

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

Arguments

:A real or complex square matrix : :H real or complex square matrix : :U orthogonal or unitary square matrix :

Description

[U,H] = hess(A) produces a unitary matrix U and a Hessenberg matrix H so that A = U*H*U’ and U’*U = Identity. By itself, hess(A) returns H.

The Hessenberg form of a matrix is zero below the first subdiagonal. If the matrix is symmetric or Hermitian, the form is tridiagonal.

References

hess function is based on the Lapack routines DGEHRD, DORGHR for real matrices and ZGEHRD, ZORGHR for the complex case.

Examples

A=`rand`_(3,3);[U,H]=hess(A);
`and`_( `abs`_(U*H*U'-A)<1.d-10 )

See Also

• qr QR decomposition
• contr controllability, controllable subspace, staircase
• schur [ordered] Schur decomposition of matrix and pencils

Used Functions

hess function is based on the Lapack routines DGEHRD, DORGHR for real matrices and ZGEHRD, ZORGHR for the complex case.