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<div style="font-size:30px">'''METZLER'''</div><br/>
<div style="font-size:30px">'''MATRIX("METZLER",order)'''</div><br/>
*<math>order</math> 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)
{| class="wikitable"
|-
| -55 || 100 || 92 || 85
|-
| 26 || 57 || 40 || 77
|-
| 5 || 40 || -33 || 11
|-
| 40 || 83 || 74 || -92
|}
*MATRIX("metzler:negzeropos",5)
{| class="wikitable"
|-
| -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
|}