Matrix Science Mathematic (MSMK)

DECOMPOSITION OF Cm THROUGH Q-PERIODIC DISCRETE EVOLUTION FAMILY

February 8, 2019 Posted by In Matrix Science Mathematic (MSMK)

ABSTRACT

DECOMPOSITION OF Cm THROUGH Q-PERIODIC DISCRETE EVOLUTION FAMILY

Journal: Matrix Science Mathematic (MSMK)
Author: Akbar Zada, Hafiz Ullah

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2019.09.12

Let U={U (m,n) : m,n ∈ Z+} n≥m≥0 be the q-periodic discrete evolution family of square size matrices of order m having complex scalars as entries generated by L(C^m-valued, q-periodic sequence of square size matrices (An)n∈Z+ where q≥2 is a natural number. Where the Poincare map U(q,0) is the generator of the discrete evolution family U. The main objective of this article to decompose C^m with the help of discrete evolution family. In fact we decompose Cm in two sub spaces X1 and X2 such that X1 is due to the stability of the discrete evolution family and the vectors of X1 will called stable vectors. While X2 is due to the un-stability of discrete evolution family, and their vectors will be called unstable vectors. More precisely we take the dichotomy of the discrete evolution family with the help of projection P on Cm and we discuss different results of the spaces X1 and X2 .
Pages 09-12
Year 2019
Issue 1
Volume 3

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