论文标题
在垂直矩阵及其代数属性上
On Vertically-Recurrent Matrices and Their Algebraic Properties
论文作者
论文摘要
在本文中，我们首先使用Pascal的三角形中的“曲棍球棒和冰球定理”的概括介绍了新的垂直矩阵。然后，我们为这些矩阵的下部三角分解提供了一个有趣的公式。在某些特殊情况下，我们还处理这些矩阵的$ M $ th功率。此外，我们提出了这些矩阵的两个重要应用，用于分解\ emph {可允许的矩阵}和矩阵，这些矩阵在\ emph {梯子网络理论中出现。 Finall，Y，我们对这些新型矩阵提出了一些开放的问题和猜想。
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.
