In this article we study quadratic forms in n independent standard normal random variables. We show that among nonnegative quadratic forms, a diagonal form with equal coefficients maximizes differential entropy when variance is fixed. As a consequence, we provide a sharp lower bound for the relative entropy between a nonnegative quadratic form and a Gaussian random variable.

翻译：在本条中,我们用独立标准正常随机变量来研究二次形式。我们显示,在非负性二次形式中,在等系数的对等形式中,当差异被固定时,对等形式会最大化差异的倍增。因此,我们为非负性二次形式和高斯随机变量之间的相对倍增线提供了一个垂直的下限。