The aim of this article is to study the minimum variance analysis (MVA) degeneration problem based on the variance space geometry. We propose a mathematical metric to evaluate the separation of the eigenvalues. In the MVA method, a variance space is obtained geometrically using an ellipsoid where the axes are equal to the square root of the eigenvalues of the covariance matrix. The metric is defined as the product between the geometric flattening of the ellipsoid with respect to the three axes. In this article, we present a statistical analysis applied to the distribution of the eigenvalue ratios and the mathematical metric focussed on the study of several interplanetary coronal mass ejections with and without magnetic clouds (MCs). The results show the non-applicability of the ratio between the intermediate and minimum eigenvalues, as well as that around 90 % $90\%$ of MC events have values in the [ 4.5 , 19.5 ] $[4.5,19.5]$ range for the defined metric. Our metric is compared with others and we show its robustness in indicating the usefulness of the MVA method to identify the axes of MCs.

中文翻译：

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行星际磁云研究中最小方差分析验证的新度量

本文的目的是研究基于方差空间几何的最小方差分析（MVA）退化问题。我们提出了一个数学度量来评估特征值的分离。在 MVA 方法中，方差空间是使用椭圆体在几何上获得的，其中轴等于协方差矩阵的特征值的平方根。该度量被定义为椭圆体相对于三个轴的几何展平之间的乘积。在本文中，我们提出了一种应用于特征值比率分布的统计分析和数学度量，重点是研究有和没有磁云 (MC) 的几种行星际日冕物质抛射。结果表明中间和最小特征值之间的比率不适用，以及大约 90 % $90\%$ 的 MC 事件的值在 [ 4.5 , 19.5 ] $[4.5,19.5]$ 范围内，用于定义的指标。我们的度量与其他度量进行了比较，我们展示了它在表明 MVA 方法用于识别 MC 轴的有用性方面的稳健性。