The Popoviciu inequality is known as a weighted version of the celebrated Aczel inequality. In this paper, we establish an analogue of the Popoviciu inequality for the determinants of positive definite matrices, and then we extend our result to the case where the underlying matrices are sectorial matrices, i.e. matrices whose field of values (or numerical range) are contained in a sector.

中文翻译：

---

行列式的 Popoviciu 型不等式

Popoviciu 不等式被称为著名的 Aczel 不等式的加权版本。在本文中，我们为正定矩阵的行列式建立了 Popoviciu 不等式的类比，然后将我们的结果扩展到基础矩阵是扇形矩阵的情况，即包含值域（或数值范围）的矩阵在一个部门。