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# hess

Hessenberg form of matrix

## Syntax

```H = hess(A) [P,H] = hess(A) [AA,BB,Q,Z] = hess(A,B) ```

## 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`.

## Examples

`H` is a 3-by-3 eigenvalue test matrix:

```H = -149 -50 -154 537 180 546 -27 -9 -25```

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

```hess(H) = -149.0000 42.2037 -156.3165 -537.6783 152.5511 -554.9272 0 0.0728 2.4489```

## More About

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### Hessenberg Matrix

A Hessenberg matrix contains zeros below the first subdiagonal. If the matrix is symmetric or Hermitian, then the form is tridiagonal. This matrix has the same eigenvalues as the original, but less computation is needed to reveal them.

## Version History

Introduced before R2006a