We provide some characterizations of the absence of triangular arbitrage in the spot exchange rates of a group of countries. When the matrix of exchange rates of the group does not fulfill the conditions given in those characterizations, we provide a measure of distance to the space of matrices of exchange rates that are triangular arbitrage-free. Using this distance, we compute the closest no-arbitrage matrix of exchange rates of the group. We apply the methodology developed to the exchange rates between the currencies of Brazil (real), European Union (euro), Great Britain (pound sterling), and USA (dollar) to analyze the possibility of triangular arbitrage in those foreign exchange markets.

中文翻译：

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汇率的无套利矩阵：一些特征

我们提供了一组国家的即期汇率中不存在三角套利的一些特征。当该组的汇率矩阵不满足这些特征中给定的条件时，我们提供了与无三角套利的汇率矩阵空间的距离度量。使用这个距离，我们计算了该组最接近的无套利汇率矩阵。我们将所开发的方法应用于巴西（雷亚尔）、欧盟（欧元）、英国（英镑）和美国（美元）之间的汇率，以分析这些外汇市场中三角套利的可能性。