PaleyI {HadamardR} | R Documentation |
This function performs constructing the Hadamard matrix by Paley method.
PaleyI(n)
n |
integer (order of the matrix) |
let q = n-1 , and q = 3 (mod 4), q is the prime number, then obtained the Hadamard matrix of order q+1.if input satisfies these condition it retuns Hadamard Matrix; otherwise returns NULL.
hadamard matrix of n
Paley, R.E.A.C. (1933). On Orthogonal matrices. J. Combin. Theory, A 57(1), 86-108.
PaleyI(8)
#' PaleyI(8)
# [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#[1,] 1 1 1 1 1 1 1 1
#[2,] -1 1 -1 -1 1 -1 1 1
#[3,] -1 1 1 -1 -1 1 -1 1
#[4,] -1 1 1 1 -1 -1 1 -1
#[5,] -1 -1 1 1 1 -1 -1 1
#[6,] -1 1 -1 1 1 1 -1 -1
#[7,] -1 -1 1 -1 1 1 1 -1
#[8,] -1 -1 -1 1 -1 1 1 1
PaleyI(16)
#NULL