# Manuals/calci/HADAMARD

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**MATRIX (TypeOfMatrix,DimensionsOfMatrix,SeedValuesToUse,IJFunction,PreParameter,IsItInternalCall)**

- is the type of the matrix.
- is the order of the Hadamard matrix.

## Description

- This function gives the matrix satisfying the property of Hadamard.
- A Hadamard matrix is the square matrix with the entries of 1 and -1.
- Also the rows of that matrix are orthogonal.
- So H be a Hadamard matrix of order 2n.
- The transpose of H is closely related to its inverse.
- The equivalent definition for hadamard matrix is:

where is the n × n identity matrix and is the transpose of H.

- So the possible order of the matrix is 1,2 or positive multiple of 4.
- The few examples of hadamard matrices are:

## Examples

- 1.MATRIX("hadamard") = 1
- 2.MATRIX("hadamard",3)

1 | 1 | 1 | 1 |

1 | -1 | 1 | -1 |

1 | 1 | -1 | -1 |

1 | -1 | -1 | 1 |

- 3.MATRIX("hadamard",4)

1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 |

1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 |

1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 |

1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 |

1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 |

1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 |

1 | -1 | -1 | 1 | -1 | 1 | 1 | -1 |

## Related Videos

## See Also

## References