Difference between revisions of "Manuals/calci/METZLER"
Jump to navigation
Jump to search
(Created page with "<div style="font-size:30px">'''METZLER'''</div><br/>") |
|||
| (2 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | <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 | ||
| + | |} | ||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/ANTIDIAGONAL| ANTIDIAGONAL]] | ||
| + | *[[Manuals/calci/CONFERENCE| CONFERENCE]] | ||
| + | *[[Manuals/calci/HANKEL| HANKEL]] | ||
| + | *[[Manuals/calci/HERMITIAN| HERMITIAN]] | ||
| + | |||
| + | ==References== | ||
| + | *[http://en.wikipedia.org/wiki/Metzler_matrix Metzler Matrix] | ||
Latest revision as of 11:04, 15 May 2015
MATRIX("METZLER",order)
- is the order of the Metzler matrix.
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 |