Manuals/calci/METZLER - Revision history

Devika at 16:04, 15 May 2015

2015-05-15T16:04:06Z

2015-04-30T15:40:20Z

Examples

2015-04-30T15:38:42Z

2015-04-30T05:12:42Z

Created page with "<div style="font-size:30px">'''METZLER'''</div><br/>"

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<div style="font-size:30px">'''METZLER'''</div><br/>

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 *[[Manuals/calci/HANKEL| HANKEL]]
 *[[Manuals/calci/HERMITIAN| HERMITIAN]]
 ==References==

← Older revision		Revision as of 15:40, 30 April 2015
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	\| 0 \|\| 1 \|\| 1 \|\| 1 \|\|1		\| 0 \|\| 1 \|\| 1 \|\| 1 \|\|1
	\|}		\|}
		+
		+	==See Also==
		+	*[[Manuals/calci/ANTIDIAGONAL\| ANTIDIAGONAL]]
		+	*[[Manuals/calci/CONFERENCE\| CONFERENCE]]
		+	*[[Manuals/calci/HANKEL\| HANKEL]]
		+	*[[Manuals/calci/HERMITIAN\| HERMITIAN]]
		+
		+
		+	==References==

← Older revision		Revision as of 15:38, 30 April 2015
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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
		+	\|}