Lower bound for the minimal eigenvalue of <i>M</i>-matrices

Abstract M -matrices have several applications in domains such as control theory, numerical analysis, optimization problems, probability, and statistics. One of the key areas of M -matrix theory is the study of minimal eigenvalues of M- matrices. The goal of this note is to introduce a better lower bound for the minimal eigenvalue of M -matrices using the special inclusion theorem for matrix eigenvalues. Two numerical tests are considered to confirm the efficiency of the new lower bound.