Abstract: The relevant properties of nonsingular M-matrices and their minimum eigenvalues are given, based on the relationship between nonnegative matrices and M-matrices. Further, the lower bound for the minimum eigenvalues of nonsingular M-matrices is given by combining the famous Gerschgorin theorem and Hölder inequality. Numerical examples are given to illustrate the effectiveness of the discussed method.

Key words: irreducible, nonsingular M-matrix, minimum eigenvalue, eigenvector