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See the recommended documentation of this function

Scilab manual >> Linear Algebra > hess

# hess

Hessenberg form

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 )

### Used Functions

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