On bounding the eigenvalues of matrices with constant row-sums

For every n × n real matrix A having as an eigenvector e, the all-ones vector, an upper bound is obtained for the absolute value of its eigenvalues except, in some cases, the one associated with e. Comparisons are made between this bound and some existing bounds for stochastic matrices as well as other types of matrices such as Laplacian matrices and Randić matrices. Other examples and results are also provided. An interesting recent article ‘An eigenvalue localization theorem for stochastic matrices and its application to Randić matrices’, Linear Algebra Appl. 2016;505:85–96, by A. Banerjee and R. Mehatari, is useful for this present paper.