منابع مشابه
Continuity Properties of the Lower Spectral Radius
The lower spectral radius, or joint spectral subradius, of a set of real d× d matrices is defined to be the smallest possible exponential growth rate of long products of matrices drawn from that set. The lower spectral radius arises naturally in connection with a number of topics including combinatorics on words, the stability of linear inclusions in control theory, and the study of random Cant...
متن کاملContinuity of the Joint Spectral Radius: Application to Wavelets
Abstract. The joint spectral radius is the extension to two or more matrices of the (ordinary) spectral radius ρ(A) = max |λi(A)| = lim‖A m‖1/m. The extension allows matrix products Πm taken in all orders, so that norms and eigenvalues are difficult to estimate. We show that the limiting process does yield a continuous function of the original matrices—this is their joint spectral radius. Then ...
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In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.
متن کاملOn spectral radius of strongly connected digraphs
It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.
متن کاملThe Sign-Real Spectral Radius for Real Tensors
In this paper a new quantity for real tensors, the sign-real spectral radius, is defined and investigated. Various characterizations, bounds and some properties are derived. In certain aspects our quantity shows similar behavior to the spectral radius of a nonnegative tensor. In fact, we generalize the Perron Frobenius theorem for nonnegative tensors to the class of real tensors.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2013
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2013-11520-0