Constant diagonal sums of doubly stochastic matrices

Abstract

The aim of this thesis is to investigate the diagonals of doubly stochastic matrices. More specifically, we have studied doubly stochastic matrices with constant diagonal sums, and how small modifications made to these matrices alter the diagonal sums. We have defined a specific operation in modifying these matrices, and found some results on how this operation alters the diagonals and diagonal sums of the matrices. Among the results, we found that the modified diagonal sums correspond to the modifications made to the matrices. In our work, we studied a specific class of doubly stochastic matrices with constant diagonal sums, in addition to randomly generated matrices using Matlab.