# Documentation

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# rosser

Classic symmetric eigenvalue test problem

## Syntax

• ``A = rosser``
example
• ``A = rosser(classname)``
example

## Description

example

````A = rosser` returns the Rosser matrix in double precision.```

example

````A = rosser(classname)` returns the Rosser matrix with a class specified by `classname`. Specify `classname` as `'single'` to return the Rosser matrix in single precision.```

## Examples

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`rosser` returns the Rosser matrix.

```rosser ```
```ans = 611 196 -192 407 -8 -52 -49 29 196 899 113 -192 -71 -43 -8 -44 -192 113 899 196 61 49 8 52 407 -192 196 611 8 44 59 -23 -8 -71 61 8 411 -599 208 208 -52 -43 49 44 -599 411 208 208 -49 -8 8 59 208 208 99 -911 29 -44 52 -23 208 208 -911 99 ```

Specify `classname` as `single` to return a Rosser matrix of that class.

```Y = rosser('single') ```
```Y = 8×8 single matrix 611 196 -192 407 -8 -52 -49 29 196 899 113 -192 -71 -43 -8 -44 -192 113 899 196 61 49 8 52 407 -192 196 611 8 44 59 -23 -8 -71 61 8 411 -599 208 208 -52 -43 49 44 -599 411 208 208 -49 -8 8 59 208 208 99 -911 29 -44 52 -23 208 208 -911 99 ```
```whos('Y') ```
``` Name Size Bytes Class Attributes Y 8x8 256 single ```

## Input Arguments

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Input class, specified as `'double'` (default) or `'single'`. `rosser(C)` produces a matrix of the specified class.

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### Rosser Matrix

The Rosser matrix is a well known matrix used, for example, to evaluate eigenvalue algorithms. The matrix is 8-by-8 with integer elements. It has:

• A double eigenvalue

• Three nearly equal eigenvalues

• Dominant eigenvalues of the opposite sign

• A zero eigenvalue

• A small, nonzero eigenvalue