MATRIX("MONOMIAL",order)
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle order}
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:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{bmatrix} 0 & 0 & 3 & 0 \\ 0 & -2 & 0 & 0 \\ 4 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix}}
- So any monomial matrix is the product of a permutation matrix and a diagonal matrix.
Examples
- 1.MATRIX("Monomial")=1
- 2.MATRIX("Monomial",3)
- 3.MATRIX("Generalized permutation",3)
- 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
|
See Also
References