A new expression for solving homogeneous linear ODEs based on a generalization of the Volterra composition was recently introduced. In this work, we extend such an expression, showing that it corresponds to inverting an infinite matrix. This is done by studying a particular subring and connecting it with a subalgebra of infinite matrices.

翻译：近期，基于沃尔泰拉复合的推广，引入了一种求解齐次线性常微分方程的新表达式。在本工作中，我们对该表达式进行了扩展，表明其对应于求逆一个无限矩阵。这是通过研究一个特定的子环，并将其与无限矩阵的子代数联系起来实现的。