PaleyII {HadamardR} | R Documentation |
This function create the Hadamard matrix by Paley method 2
PaleyII(n)
n |
integer(order of the matrix) |
q=n/2-1, If there is an Hadamard matrix of order h>1, and q = 1 (mod 4) is a prime number, then there exists an Hadamard matrix of order nh.
Hadamard matrix of order n
Paley, R.E.A.C. (1933). On Orthogonal matrices. J. Combin. Theory, A 57(1), 86-108.
PaleyII(12)
# [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
# [1,] 1 1 1 1 1 1 1 -1 -1 -1 -1 -1
# [2,] 1 1 1 -1 -1 1 -1 1 -1 1 1 -1
# [3,] 1 1 1 1 -1 -1 -1 -1 1 -1 1 1
# [4,] 1 -1 1 1 1 -1 -1 1 -1 1 -1 1
# [5,] 1 -1 -1 1 1 1 -1 1 1 -1 1 -1
# [6,] 1 1 -1 -1 1 1 -1 -1 1 1 -1 1
# [7,] 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
# [8,] -1 1 -1 1 1 -1 -1 -1 -1 1 1 -1
# [9,] -1 -1 1 -1 1 1 -1 -1 -1 -1 1 1
#[10,] -1 1 -1 1 -1 1 -1 1 -1 -1 -1 1
#[11,] -1 1 1 -1 1 -1 -1 1 1 -1 -1 -1
#[12,] -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1
PaleyII(8)
#NULL