Corrigendum/addendum to: Sets of matrices all infinite products of which converge (original) (raw)
Related papers
On Topological Semigroups of Matrix Units
Semigroup Forum, 2005
On the infinite semigroup of matrix units there exists no semigroup compact [countably compact] topology. Any continuous homomorphism from the infinite topological semigroup of matrix units into a compact topological semigroup is annihilating. The semigroup of matrix units is algebraically h -closed in the class of topological inverse semigroups. Some H -closed minimal semigroup topologies on the infinite semigroup of matrix units are considered.
Semigroup Forum, 1971
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Sets of matrices all infinite products of which converge
Linear Algebra and its Applications, 1992
An infinite product IIT= lMi of matrices converges (on the right) if limi __ M, . . . Mi exists. A set Z = (Ai: i > l} of n X n matrices is called an RCP set (rightconvergent product set) if all infinite products with each element drawn from Z converge. Such sets of matrices arise in constructing self-similar objects like von Koch's snowflake curve, in various interpolation schemes, in constructing wavelets of compact support, and in studying nonhomogeneous Markov chains. This paper gives necessary conditions and also some sufficient conditions for a set X to be an RCP set. These are conditions on the eigenvalues and left eigenspaces of matrices in 2 and finite products of these matrices. Necessary and sufficient conditions are given for a finite set Z to be an RCP set having a limit function M,(d) = rIT= lAd,, where d = (d,, . , d,, . .>, which is a continuous function on the space of all sequences d with the sequence topology. Finite RCP sets of column-stochastic matrices are completely characterized. Some results are given on the problem of algorithmically deciding if a given set X is an RCP set.
On semigroups of matrices with nonnegative diagonals
2013
We give a short proof of a recent result by Bernik, Mastnak, and Radjavi, stating that an irreducible group of complex matrices with nonnegative diagonal entries is diagonally similar to a group of nonnegative monomial matrices. We also explore the problem when an irreducible matrix semigroup in which each member is diagonally similar to a nonnegative matrix is diagonally similar to a semigroup of nonnegative matrices.
Matrix semigroups with constant spectral radius
Linear Algebra and its Applications
Multiplicative matrix semigroups with constant spectral radius (c.s.r.) are studied and applied to several problems of algebra, combinatorics, functional equations, and dynamical systems. We show that all such semigroups are characterized by means of irreducible ones. Each irreducible c.s.r. semigroup defines walks on Euclidean sphere, all its nonsingular elements are similar (in the same basis) to orthogonal. We classify all nonnegative c.s.r. semigroups and arbitrary low-dimensional semigroups. For higher dimensions, we describe five classes and leave an open problem on completeness of that list. The problem of algorithmic recognition of c.s.r. property is proved to be polynomially solvable for irreducible semigroups and undecidable for reducible ones.
On finiteness conditions for Rees matrix semigroups
Czechoslovak Mathematical Journal, 2005
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
On the Infinite Products of Matrices
Advances in Pure Mathematics, 2012
In different fields in space researches, Scientists are in need to deal with the product of matrices. In this paper, we develop conditions under which a product of matrices chosen from a possibly infinite set of matrices 0 i i