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# hadamard

Hadamard matrix

## Syntax

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

## Description

example

``H = hadamard(n) ` returns the Hadamard Matrix of order `n`.`
````H = hadamard(n,classname)` returns a matrix of class `classname`, which can be either `'single'` or `'double'`.```

## Examples

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Compute the 4-by-4 Hadamard matrix.

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

## Input Arguments

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Matrix order, specified as a scalar, nonnegative integer.

Example: `hadamard(4)`

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

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

Example: `hadamard(4,'single')`

Data Types: `char`

## Limitations

• 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.

## More About

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### Hadamard Matrix

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 , .

 Ryser, Herbert J. Combinatorial Mathematics. Mathematical Association of America, 1963.

 Pratt, William K. Digital Signal Processing. New York, NY: John Wiley and Sons, 1978.

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