# Documentation

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## Syntax

`H = hadamard(n)`

## Description

`H = hadamard(n)` returns the Hadamard matrix of order `n`.

## Definitions

Hadamard matrices are matrices of `1`'s and `-1`'s whose columns are orthogonal,

```H'*H = n*I ```

where `[n n]=size(H)` and `I = eye(n,n)`.

They have applications in several different areas, including combinatorics, signal processing, and numerical analysis, [1], [2].

An `n`-by-`n` Hadamard matrix with `n > 2` exists only if `rem(n,4)` `=` `0`. This function handles only the cases where `n`, `n/12`, or `n/20` is a power of 2.

## Examples

collapse all

Compute the 4-by-4 Hadamard matrix.

```H = hadamard(4) ```
```H = 1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 -1 -1 1 ```

## References

[1] Ryser, H. J., Combinatorial Mathematics, John Wiley and Sons, 1963.

[2] Pratt, W. K., Digital Signal Processing, John Wiley and Sons, 1978.