Technical Report CS-2018-03

Title: On the Analytical Structure of a Vector Sequence Generated via a Linear Recursion
Authors: Avram Sidi
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Abstract: In this note, we discuss the nature of a vector sequence $\{\ff_n\}^\infty_{n=0}\in \C^N$ generated by a linear recursion of the form $$\sum^m_{j=0}\AAA_j\ff_{k+j}=\00,\quad k=0,1,\ldots,$$ where $ \AAA_j\in\mathbb{C}^{N\times N},$ $j=0,1,\ldots,m,$ $\AAA_m$ is nonsingular, and $\AAA_0\neq \OO.$ We also discuss the nature of the function $\ff(z)$ that is defined by the infinite series $\sum^\infty_{n=0}\ff_nz^n$.

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