As one application of the Cauchy–Binet formula, the Ball–Barthe inequality plays a key role in solving reverse isoperimetric inequalities. Recently, a new Grassmannian Ball–Barthe inequality was established. With it, reverse isoperimetric inequalities on Grassmann manifolds were successfully proved. In this paper, we will establish its matrix form with a simpler proof than that of Grassmannian form. The matrix form also recovers the classical Ball–Barthe inequality in a special case.

中文翻译：

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Grassmannian Ball–Barthe 不等式的矩阵形式

Ball-Barthe不等式作为Cauchy-Binet公式的一个应用，在求解逆等周不等式中起着关键作用。最近，建立了一个新的格拉斯曼球-巴特不等式。以此成功证明了格拉斯曼流形上的逆等周不等式。在本文中，我们将通过比格拉斯曼形式更简单的证明来建立它的矩阵形式。在特殊情况下，矩阵形式也恢复了经典的 Ball–Barthe 不等式。