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Supported by the National Natural Science Foundation of China under grant 10871051, Shanghai Municipal Science & Technology Committee under grant 09DZ2272900, Shanghai

It turns out that most properties of classical Bezoutians can be analogously generalized to the case of polynomial Bezoutians in the framework of algebraic methods..

The first group is about spectral properties of a matrix under such perturbations; the second is about almost-near relations with respect to the rank distance..

In this paper, by using majorization inequalities, upper bounds on summations of eigenvalues (including the trace) of the solution for the Lyapunov matrix differential equation

This work was supported in part by the National Natural Science Foundation of China 10971176, the Guangdong Provincial Natural Science Foundation of China 10152104101000008 and the

Research was supported in part by the Faculty Research Assignment and Plumeri Award at the College of William and Mary. Electronic Journal of Linear Algebra ISSN 1081-3810

Furthermore, the criterion applies to two important classes of branching random walks and implies that the critical branching random walk is transient resp.. dies

We also show that the emergence of giant cycles coincides with a phase transition in the acceleration of the random walk, as measured by the second derivative of the distance (on