In this paper, we study the sequences of matrix Cauchy biorthogonal polynomials. We will focus on the algebraic aspects of the problem, finding a connection with a kind of matrix mixed-type Hermite–Padé approximation problem and a Riemann–Hilbert problem. From here, we deduce some properties of these families of matrix Cauchy biorthogonal polynomials.

中文翻译：

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关于矩阵柯西双正交多项式

在本文中，我们研究了矩阵柯西双正交多项式的序列。我们将专注于问题的代数方面，寻找与一种矩阵混合型 Hermite-Padé 近似问题和 Riemann-Hilbert 问题的联系。从这里，我们推导出这些矩阵柯西双正交多项式族的一些性质。