The NIEP for four dimensional Leslie and doubly stochastic matrices with zero trace from the coefficients of the characteristic polynomial

The constraints on the coefficients of the characteristic polynomials of four dimensional doubly stochastic matrices with zero trace and Leslie stochastic matrices with zero trace are determined. Then, on the basis of these constraints, the regions of the complex plane consisting of those points which can serve as characteristic roots of four dimensional doubly stochastic matrices with zero trace and Leslie stochastic matrices with zero trace are characterized

A Cycle-Based Bound for Subdominant Eigenvalues of Stochastic Matrices

Given a primitive stochastic matrix, we provide an upper bound on the moduli of its non-Perron eigenvalues. The bound is given in terms of the weights of the cycles in the directed graph associated with the matrix. The bound is attainable in general, and we characterize a special case of equality when the stochastic matrix has a positive row. Applications to Leslie matrices and to Google-type matrices are also considere

A Cycle-Based Bound for Subdominant Eigenvalues of Stochastic Matrices

Given a primitive stochastic matrix, we provide an upper bound on the moduli of its non-Perron eigenvalues. The bound is given in terms of the weights of the cycles in the directed graph associated with the matrix. The bound is attainable in general, and we characterize a special case of equality when the stochastic matrix has a positive row. Applications to Leslie matrices and to Google-type matrices are also considere