Wasserstein distances in optimal transport provides a mathematical tool to measure distances between functions or more general objects. By Wasserstein distances, we define a distance on the moduli space of a class of statistical manifolds. We construct a Riemannian metric of this space and verify that the defined distance can be regarded as the induced distance of the metric.
For the Hadamard product of the matrices with non-negative entries, we study the new upper bound for the spectral radius by applying the characteristic value containing the domain theorem. This estimating formula only involves the entries of two non-negative matrices. Hence, the upper bound is easy to calculate in practical examples. An example is considered to illustrate our results.
According to the related M-matrix property, new upper bounds for the minimum eigenvalue of the irreducible M-matrix are provided. It is demonstrated that the new upper bound is sharper than the classical upper bound when the M-matrix is symmetric. Numerical examples further verify the validity of the results.
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