MATLAB Function Reference |

**Syntax**

**Description**

```
H = hadamard(n)
```

returns the Hadamard matrix of order `n`

.

**Definition**

Hadamard matrices are matrices of `1`

's and `-1`

's whose columns are orthogonal,

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**

The command `hadamard(4)`

produces the 4-by-4 matrix:

**See Also**

**References**

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

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

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