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.