# Manuals/calci/METZLER

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**MATRIX("METZLER",order)**

- is the order of the Metzler matrix.

## Description

- This function gives the matrix of order 3 with the metzler properties.
- A matrix is called Metzler if all of its elements are non-negative except for those on the main diagonal, which are unconstrained.
- i.e., The off diagonal values must be "+" and main diagonal values "+","-" or "0".
- Also Metzler is also called as quasi positive or essentially nonnegative.
- The exponential of a Metzler matrix is a nonnegative matrix because of the corresponding property for the exponential of a nonnegative matrix.
- A Metzler matrix has an eigenvector in the nonnegative matrix because of the corresponding property for nonnegative matrices.
- In Calci, users need a metzler matrix with various values, then the syntax is MATRIX("metzler").
- Otherwise users need a matrix with values 0,1 and -1, then the syntax is : MATRIX("metzler:negzeropos")

## Examples

- MATRIX("metzler",4)

-55 | 100 | 92 | 85 |

26 | 57 | 40 | 77 |

5 | 40 | -33 | 11 |

40 | 83 | 74 | -92 |

- MATRIX("metzler:negzeropos",5)

-1 | 1 | 1 | 0 | 1 |

1 | 1 | 1 | 0 | 1 |

1 | 1 | -1 | 1 | 0 |

0 | 1 | 1 | 0 | 1 |

0 | 1 | 1 | 1 | 1 |