MATRIX("MOORE",order)
- is the size of the Moore matrix.
is the size of the Moore matrix.Description
- This function gives the moore matrix of order 3 with the element 1.
- A moore matrix, is a square matrix over a finite field.
- When moore matrix is a square matrix, then its deteminant is called a Moore determinant.
- But it is unrelated to the Moore determinant of a quaternionic Hermitian matrix.
- The Moore matrix has successive powers of the applied to the first column, so it is an mxn matrix of the form:
Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: Double exponent: use braces to clarify"): {\displaystyle {\begin{bmatrix}\alpha _{1}&{\alpha _{1}}^{q}&\cdots &{\alpha _{1}}^{q}^{n-1}\\\alpha _{2}&{\alpha _{2}}^{q}&\cdots &{\alpha _{2}}^{q}^{n-1}\\\alpha _{3}&{\alpha _{3}}^{q}&\cdots &{\alpha _{3}}^{q}^{n-1}\\\vdots &\ddots &\vdots \\\alpha _{m}&{\alpha _{m}}^{q}&\cdots &{\alpha _{m}}^{q}^{n-1}\\\end{bmatrix}}}
- In calci, MATRIX("moore") is giving the matrixwith the element 1 of order 3.
- And MATRIX("moore",4,1..4) is giving Moore matrix starting element 1 to 4 of order 4.
Examples
- 1.MATRIX("moore")
| 1 | 1 | 1 |
| 1 | 1 | 1 |
| 1 | 1 | 1 |
- 2.MATRIX("moore",5,1..5)
| 1 | 1 | 1 | 1 | 1 |
| 2 | 4 | 16 | 256 | 65536 |
| 3 | 9 | 81 | 6561 | 43046721 |
| 4 | 16 | 256 | 65536 | 4294967296 |
| 5 | 25 | 625 | 390625 | 152587890625 |
- 3.MATRIX("moore",4,3..7,"",2.3)
| 3 | 12.513502532843182 | 334.1730615222005 | 638460.9005874459 |
| 4 | 24.251465064166364 | 1530.7256306021752 | 21147737.669320222 |
| 5 | 40.51641491731905 | 4983.693475030862 | 319424366.94628483 |
| 6 | 61.623714938749366 | 13074.350231574774 | 2936069039.087338 |
See Also