Find the eigenvector: Let S be n*n square matrix w/ all non-zero elements. The sum of each row's elements is equal to 1.

[spinos]

Hello, could you help me to find the eigenvector of this problem?

Let S be an n*n square matrix with all non-zero elements. The sum of the elements of each row is equal to 1. Find an eigenvalue of and an eigenvector of the matrix S as well as one of \(\displaystyle S^2\)

 

[blamocur]

If you only need to find one eigenvalue and the corresponding eigenvector then use the fact that computing sums of each row is equivalent by multiplying the matrix by a vector (on the right).