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# hess

Hessenberg form

### Syntax

```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.

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