Select Page
[Total: 0    Average: 0/5]
As a basic tool of the experience plans, the Hadamard matrices have allowed to “automate” the planning of the experiments while guaranteeing the quality of the mathematical result.

## Introduction

The plans of experiments are all based on the matrixes of Hadamard. These matrices were invented by Sylvester in 18671, which built of any order, a power of 2, thanks to his idea of doubling. Hadamard, a famous French mathematician known for his first-number theorem, built of order 12 and 20 and formulated his famous conjecture in 1893: ” for any n multiple of 4, there is a matrix of Hadamard of order n”. A Hadamard array of order N is an array with n rows and n columns such as:

• All its coefficients are worth-1 or + 1
• For each pair of lines, there are as many concordances as inconsistencies, i.e. columns where the coefficients are equal, and columns where the coefficients are distinct.

In other words, in the following matrix where n = 8, take two lines, and count the columns whose two squares are of the same color, that is, both white or both orange. So we find exactly 4 color matches , and thus automatically 4 color discrepancies .

Hadamard matrix with n = 8 Lines 1 and 2 of the logo

The color matches are in columns 1, 3, 5 and 7, and the discrepancies in the remaining four columns. Lines 3 and 5 of the logo

Color matches are held here in columns 1, 2, 7 and 8. 