While matrices are usually used as the basic data structure for experiments with repeated measurements or longitudinal data, testing methods for the equality of two matrix distributions have not been fully discussed in the literature. In this article, we propose three methods to test the equality of two matrix distributions: the likelihood ratio test, the Frobenius norm methods and triangle tests. We present a simulation to compare their performance under the matrix normal distribution. We apply the testing methods to compare the US economy, as measured by closing prices of five market indices, before and after the US stock market crash of 2008.

中文翻译：

---

测试矩阵分布是否相等

虽然矩阵通常用作重复测量或纵向数据实验的基本数据结构，但文献中尚未充分讨论两种矩阵分布相等性的测试方法。在本文中，我们提出了三种方法来检验两个矩阵分布的相等性：似然比检验，Frobenius范数方法和三角检验。我们提出了一个模拟，以比较它们在矩阵正态分布下的性能。我们采用测试方法对美国经济进行比较，以五种市场指数在2008年美国股市崩盘前后的收盘价来衡量。