Euclidean distance matrices ($\mathrm{EDM}$) are symmetric nonnegative matrices with several interesting properties. In this article, we introduce a wider class of matrices called generalized Euclidean distance matrices ($\mathrm{GEDM}$s) that include $\mathrm{EDM}$s. Each $\mathrm{GEDM}$ is an entry-wise nonnegative matrix. A $\mathrm{GEDM}$ is not symmetric unless it is an $\mathrm{EDM}$. By some new techniques, we show that many significant results on Euclidean distance matrices can be extended to generalized Euclidean distance matrices. These contain results about eigenvalues, inverse, determinant, spectral radius, Moore–Penrose inverse and some majorization inequalities. We finally give an application by constructing infinitely divisible matrices using generalized Euclidean distance matrices.

欧氏距离矩阵 ($\mathrm{电火花加工}$) 是具有几个有趣属性的对称非负矩阵。在本文中，我们介绍了一类更广泛的矩阵，称为广义欧几里得距离矩阵（$\mathrm{全球发展管理委员会}$s) 包括$\mathrm{电火花加工}$秒。每个$\mathrm{全球发展管理委员会}$是逐项非负矩阵。A$\mathrm{全球发展管理委员会}$不是对称的，除非它是$\mathrm{电火花加工}$. 通过一些新技术，我们表明欧氏距离矩阵上的许多重要结果可以扩展到广义欧氏距离矩阵。这些包含关于特征值、逆、行列式、谱半径、Moore-Penrose 逆和一些主要化不等式的结果。最后给出一个应用，用广义欧氏距离矩阵构造无限可分矩阵。