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?
