Nonnegativity of the second largest eigenvalue of 4 × 4 tridiagonal stochastic matrices
Abstract
The spectral study of nonnegative and more specifically stochastic matrices is an important topic in matrix theory. In this paper, we prove a conjecture, formulated by Ran and Teng, which states that the second largest eigenvalue of an irreducible 4×4 tridiagonal stochastic matrix is nonnegative. We establish this conjecture and extend the result to arbitrary 4×4 tridiagonal stochastic matrices, including both irreducible and reducible cases.
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