Abstract:In this article, we take a geometric approach to extend Newton's well-known inequalities. A family of inequalities, which are invariant under affine transformations, is proposed for parallelotopes. We prove some of them and show the connections they have with matrix inequalities, convex geometry, and geometric inequalities.

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中文翻译：

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几何牛顿不等式

摘要：在本文中，我们采用几何方法来扩展牛顿众所周知的不等式。提出了在仿射变换下不变的一族不等式。我们证明其中一些，并显示它们与矩阵不等式，凸几何和几何不等式的联系。

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