kronecker_matrix {HadamardR}

kronecker_matrix

Description

kronecker_matrix

Usage

kronecker_matrix(n)

Arguments

n

integer (order of the matrix)

Details

This function construct Hadamard matrix by multiple of 2 Hadamard matrix. It Returns the Hadamard Matrix, if it is not possible NULL is returned.

Value

Hadamard matrix of order "n"

References

Sylvester, J.J. (1967). Thoughts on orthogonal matrices, simultaneous sign-succession and Tessellated pavements in two or more colours, with applications to Newton's rule, ornamental Tie-work, and the theory of numbers. Phil. Mag.,34, 461-475.

Sylvester, J.J. (1968). Problem 2511. Math. Questions and solutions, 10, 74.

Hedayat, A. and Wallis, W.D. (1978). Hadamard Matrices and Their Application.Ann. Stat., 6, 1184-1238.

Examples

kronecker_matrix(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
kronecker_matrix(12)
#NULL