Manuals/calci/METZLER

MATRIX("METZLER",order)

• $order$ 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