Difference between revisions of "Manuals/calci/MONOMIAL"
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| − | <div style="font-size:30px">'''MONOMIAL'''</div><br/> | + | <div style="font-size:30px">'''MATRIX("MONOMIAL",order)'''</div><br/> |
| + | *<math>order</math> is the order of the Monomial matrix. | ||
| + | |||
| + | ==Description== | ||
| + | *This function gives the matrix of order 3 with the property of monomial matrix. | ||
| + | *A monomial matrix is a square matrix with exactly one nonzero entry in each row and exactly one nonzero entry in each column. | ||
| + | *So here MATRIX("monomial") is showing the monomial matrix of order 3. | ||
| + | *Monomial matrix is also called as generalized permutation matrix. | ||
| + | *So in Calci, users can give the argument as MATRIX("Monomial") or MATRIX(" generalized permutation"). | ||
| + | *An example of monomial or generalized permutation matrix is: | ||
| + | <math>\begin{bmatrix} | ||
| + | 0 & 0 & 3 & 0 \\ | ||
| + | 0 & -2 & 0 & 0 \\ | ||
| + | 4 & 0 & 0 & 0 \\ | ||
| + | 0 & 0 & 0 & 1 \\ | ||
| + | \end{bmatrix}</math> | ||
| + | *So any monomial matrix is the product of a permutation matrix and a diagonal matrix. | ||
| + | |||
| + | ==Examples== | ||
| + | *1.MATRIX("Monomial")=1 | ||
| + | *2.MATRIX("Monomial",3) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 0 || 0 || 3 | ||
| + | |- | ||
| + | | 2 || 0 || 0 | ||
| + | |- | ||
| + | | 0 || 1 || 0 | ||
| + | |} | ||
| + | *3.MATRIX("Generalized permutation",3) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 0 || 3 || 0 | ||
| + | |- | ||
| + | | 3 || 0 || 0 | ||
| + | |- | ||
| + | | 0 || 0 || 2 | ||
| + | |} | ||
| + | *4.MATRIX("generalized permutation",5,-10..-2) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 0 || 0 || 0 || -10 || 0 | ||
| + | |- | ||
| + | | 0 || -9 || 0 || 0 || 0 | ||
| + | |- | ||
| + | | 0 || 0 || -8 || 0 || 0 | ||
| + | |- | ||
| + | | 0 || 0 || 0 || 0 || -7 | ||
| + | |- | ||
| + | | -6 || 0 || 0 || 0 || 0 | ||
| + | |} | ||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/HADAMARD| HADAMARD]] | ||
| + | *[[Manuals/calci/EXCHANGE| EXCHANGE]] | ||
| + | *[[Manuals/calci/IDENTITY| IDENTITY]] | ||
| + | *[[Manuals/calci/HANKEL| HANKEL]] | ||
| + | |||
| + | ==References== | ||
| + | *[http://en.wikipedia.org/wiki/Generalized_permutation_matrix Generalized Permutation Matrix] | ||
Latest revision as of 02:27, 26 October 2015
MATRIX("MONOMIAL",order)
- is the order of the Monomial matrix.
is the order of the Monomial matrix.Description
- This function gives the matrix of order 3 with the property of monomial matrix.
- A monomial matrix is a square matrix with exactly one nonzero entry in each row and exactly one nonzero entry in each column.
- So here MATRIX("monomial") is showing the monomial matrix of order 3.
- Monomial matrix is also called as generalized permutation matrix.
- So in Calci, users can give the argument as MATRIX("Monomial") or MATRIX(" generalized permutation").
- An example of monomial or generalized permutation matrix is:
- So any monomial matrix is the product of a permutation matrix and a diagonal matrix.
Examples
- 1.MATRIX("Monomial")=1
- 2.MATRIX("Monomial",3)
| 0 | 0 | 3 |
| 2 | 0 | 0 |
| 0 | 1 | 0 |
- 3.MATRIX("Generalized permutation",3)
| 0 | 3 | 0 |
| 3 | 0 | 0 |
| 0 | 0 | 2 |
- 4.MATRIX("generalized permutation",5,-10..-2)
| 0 | 0 | 0 | -10 | 0 |
| 0 | -9 | 0 | 0 | 0 |
| 0 | 0 | -8 | 0 | 0 |
| 0 | 0 | 0 | 0 | -7 |
| -6 | 0 | 0 | 0 | 0 |