Periodicity of infinite products of matrices with some negative elements and row sums equal to one (original) (raw)

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

Discrete period matrices and related topics

2001

We continue our investigation of Discrete Riemann Surfaces with the discussion of the discrete analogs of period matrices, Riemann's bilinear relations, exponential of constant argument, series and electrical moves. We show that given a refining sequence of critical maps, the discrete period matrix converges to the continuous one.

On Convergent Infinite Products and Some Generalized Inverses of Matrix Sequences

The definition of convergence of an infinite product of scalars is extended to the infinite usual and Kronecker products of matrices. The new definitions are less restricted invertibly convergence. Whereas the invertibly convergence is based on the invertible of matrices; in this study, we assume that matrices are not invertible. Some sufficient conditions for these kinds of convergence are studied. Further, some matrix sequences which are convergent to the Moore-Penrose inverses A and outer inverses A 2 T,S as a general case are also studied. The results are derived here by considering the related well-known methods, namely, Euler-Knopp, Newton-Raphson, and Tikhonov methods. Finally, we provide some examples for computing both generalized inverses A 2 T,S and A numerically for any arbitrary matrix A m,n of large dimension by using MATLAB and comparing the results between some of different methods.

On Convergents Infinite Products and Some Generalized Inverses of Matrix Sequences

Abstract and Applied Analysis, 2011

The definition of convergence of an infinite product of scalars is extended to the infinite usual and Kronecker products of matrices. The new definitions are less restricted invertibly convergence. Whereas the invertibly convergence is based on the invertible of matrices; in this study, we assume that matrices are not invertible. Some sufficient conditions for these kinds of convergence are studied. Further, some matrix sequences which are convergent to the Moore-Penrose inversesA+and outer inversesAT,S(2)as a general case are also studied. The results are derived here by considering the related well-known methods, namely, Euler-Knopp, Newton-Raphson, and Tikhonov methods. Finally, we provide some examples for computing both generalized inversesAT,S(2)andA+numerically for any arbitrary matrixAm,nof large dimension by using MATLAB and comparing the results between some of different methods.

On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of Matrices

Discrete Dynamics in Nature and Society, 2018

We consider the problem of convergence to zero of matrix products AnBn • • • A1B1 with factors from two sets of matrices, Ai ∈ A and Bi ∈ B, due to a suitable choice of matrices {Bi}. It is assumed that for any sequence of matrices {Ai} there is a sequence of matrices {Bi} such that the corresponding matrix product AnBn • • • A1B1 converges to zero. We show that in this case the convergence of the matrix products under consideration is uniformly exponential, that is, AnBn • • • A1B1 ≤ Cλ n , where the constants C > 0 and λ ∈ (0, 1) do not depend on the sequence {Ai} and the corresponding sequence {Bi}. Other problems of this kind are discussed and open questions are formulated.

Invertibility and inversion of linear periodic systems

Automatica, 1992

In this paper the invertibility properties of periodic discrete-time systems are studied. Necessary and sufficient conditions for the existence and a synthesis procedure for constructing left and right inverses are given.

Almost convergence and generalized difference matrix

Computers & Mathematics With Applications, 2011

Matrix domain of a sequence space βand γ -duals and matrix transformations a b s t r a c t Let f denotes the space of almost convergent sequences introduced by Lorentz [G.G.