MATLAB Function Reference |

**Syntax**

**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:

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

**Algorithm**

`hess`

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

**See Also**

**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* (http://www.netlib.org/lapack/lug/
lapack_lug.html), Third Edition, SIAM, Philadelphia, 1999.

helpwin | hex2dec |