In this paper, a novel method is presented to compute an explicit formula for the inverse of the confluent Vandermonde matrices. The proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences, notably on the situations where the Vandermonde matrices have acquired much usefulness. The method presented here is direct and straightforward, it gives explicit and compact formulas. Several examples are presented to highlight the results. The main tools are some elementary basic linear algebra.

中文翻译：

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一种通过泰勒展开计算合流 Vandermonde 矩阵逆的新方法

在本文中，提出了一种计算合流 Vandermonde 矩阵逆的显式公式的新方法。所提出的结果可能在数学和自然科学的不同领域有许多有趣的观点，特别是在 Vandermonde 矩阵获得很多有用的情况下。这里介绍的方法直接明了，它给出了明确而紧凑的公式。提供了几个例子来突出结果。主要工具是一些初等基础线性代数。