Manuals/calci/MOORE

MATRIX("MOORE",order)

• $order$ 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

• ANTIDIAGONAL
• CONFERENCE
• HANKEL
• HERMITIAN