An annotated bibliography on convergence of matrix products and the theory of joint/generalized spectral radius
نویسنده
چکیده
This is an attempt to systematize my personal knowledge about convergence of infinite matrix products and the rate of their growth/decrease when the number of multipliers tends to infinity.
منابع مشابه
Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra
In this paper, we discuss some properties of joint spectral {radius(jsr)} and generalized spectral radius(gsr) for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...
متن کاملOn explicit a priori estimates of the joint spectral radius by the generalized Gelfand formula
In various problems of control theory, non-autonomous and multivalued dynamical systems, wavelet theory and other fields of mathematics information about the rate of growth of matrix products with factors taken from some matrix set plays a key role. One of the most prominent quantities characterizing the exponential rate of growth of matrix products is the so-called joint or generalized spectra...
متن کاملCartesian decomposition of matrices and some norm inequalities
Let X be an n-square complex matrix with the Cartesian decomposition X = A + i B, where A and B are n times n Hermitian matrices. It is known that $Vert X Vert_p^2 leq 2(Vert A Vert_p^2 + Vert B Vert_p^2)$, where $p geq 2$ and $Vert . Vert_p$ is the Schatten p-norm. In this paper, this inequality and some of its improvements ...
متن کاملA Rapidly-converging Lower Bound for the Joint Spectral Radius via Multiplicative Ergodic Theory
We use ergodic theory to prove a quantitative version of a theorem of M. A. Berger and Y. Wang, which relates the joint spectral radius of a set of matrices to the spectral radii of finite products of those matrices. The proof rests on a theorem asserting the existence of a continuous invariant splitting for certain matrix cocycles defined over a minimal homeomorphism and having the property th...
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 $nge 4$.
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تاریخ انتشار 2013