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))`

.

`[AA,BB,Q,Z] = HESS(A,B)`

for square matrices `A`

and `B`

, produces an upper Hessenberg matrix `AA`

, an upper triangular matrix `BB`

, and unitary matrices `Q`

and `Z`

such that `Q*A*Z = AA`

and `Q*B*Z = BB`

.

**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:

**Inputs of Type Double**

For inputs of type double, `hess`

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

**Inputs of Type Single**

For inputs of type `single`

, `hess`

uses the following 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.

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