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 (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} \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.