Does this conjecture lead us toward an absolute justice in the world?

Eigenvalue equal to the sum of all elements on each column or row

One of the properties two ways matrices which can be easily proved is, to obtain the Eigenvalue where the sum of all elements on each column or row is equal to Eigenvalue of these matrices.

Another interesting property of a two way matrix is, to have a special eigenvector that all elements of it are the same. It means, if “M” is a two ways matrix, vector “V” will be eigenvector of matrix “M” where we have:

V = (x, x, x, x, ….)  and    λ = the sum of all elements on each column or row

This property can be easily proved. 

Following to article of “The Impact of Stochastic Matrix on Any Vector”, let me tell you about another conjecture as follows:

Conjecture (2): The final result of Markov Process including the impact of a two ways stochastic matrix on any vector will be a vector with the same elements where each element will be equal to average all elements of initial vector.

Initial Vector: V0 = (a, b, c, d,….) and M = two ways stochastic matrix

Example:

Does this conjecture lead us toward an absolute justice in the world?