Matrices of order relations

The order relation corresponds to matrices in which the main diagonal is filled with units (reflexivity). For each pair of unit elements, one of which is located in the Ith column and the Jth row, and the second in the Jth column and the Kth row, there is necessarily a single element in the Ith column and Kth row ( transitivity). In addition, no single element has a symmetric with respect to the main diagonal (antisymmetry).

The matrix of strict order relations is different in that all elements of the main diagonal are zero (anti-reflexivity).

For example : The matrix of the relation “to be a divisor” on the set M = {1, 2, 3, 4, 6, 7, 12, 14} has the form:

The matrix of relations “to be larger” on the set M = {1, 4, 2, 6, 3, 7, 8, 10} has the form:

· If a set of a completely strict order is set on the set M , i.e. M = {1, 2, 3, 4, 6, 7, 8, 10}, then the “be bigger” ratio matrix on this set has units in all cells located below the main diagonal, and zeros in all cells located above the main diagonal.