# hilb

Hilbert matrix

## Syntax

``H = hilb(n)``
``H = hilb(n,classname)``

## Description

example

````H = hilb(n)` returns the Hilbert matrix of order `n`. The Hilbert matrix is a notable example of a poorly conditioned matrix. The elements of Hilbert matrices are given by H(i,j) = 1/(i + j – 1).```
````H = hilb(n,classname)` returns a matrix of class `classname`, which can be either `'single'` or `'double'`.```

## Examples

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Compute the fourth-order Hilbert matrix and its condition number to see that it is poorly conditioned.

`H = hilb(4)`
```H = 4×4 1.0000 0.5000 0.3333 0.2500 0.5000 0.3333 0.2500 0.2000 0.3333 0.2500 0.2000 0.1667 0.2500 0.2000 0.1667 0.1429 ```
`cond(H)`
```ans = 1.5514e+04 ```

## Input Arguments

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Matrix order, specified as a scalar, nonnegative integer.

Example: `hilb(10)`

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `logical`

Matrix class, specified as either `'double'` or `'single'`.

Example: `hilb(10,'single')`

Data Types: `char`

 Forsythe, G. E. and C. B. Moler. Computer Solution of Linear Algebraic Systems. Englewood Cliffs, NJ: Prentice-Hall, 1967.