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arXiv · 2206.02758

On Vertically-Recurrent Matrices and Their Algebraic Properties

Hossein Teimoori Faal
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Abstract

In this paper, we first introduce the new class of vertically-recurrent matrices, using a generalization of "the Hockey stick and Puck theorem" in Pascal's triangle. Then, we give an interesting formula for the lower triangular decomposition of these matrices. We also deal with the $m$-th power of these matrices in some special cases. Furthermore, we present two important applications of these matrices for decomposing \emph{admissible matrices} and matrices which arise in the theory of \emph{ladder networks}. Finall,y we pose some open problems and conjectures about these new kind of matrices.

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Hossein Teimoori Faal. 2022-06-06. On Vertically-Recurrent Matrices and Their Algebraic Properties. https://arxiv.org/abs/2206.02758

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