Abstract This work describes periodic matrices in the general linear group over the real numbers field and over the maximal Abelian extension ?ab of the rational numbers field. It is shown that for the case of real numbers the general question is reduced to the 2×2 matrices. A simple periodicity criterion is provided for them. We demonstrate a geometric interpretation of the results. The main result is an algorithm that tests periodicity of a matrix and, if the matrix is periodic, finds its Jordan form.
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机译：摘要 本文描述了在实数域和有理数域的最大阿贝尔扩展？ab上的一般线性群中的周期矩阵。结果表明，对于实数的情况，一般问题简化为 2×2 矩阵。为它们提供了一个简单的周期性标准。我们演示了结果的几何解释。主要结果是一种算法，该算法测试矩阵的周期性，如果矩阵是周期性的，则找到其 Jordan 形式。
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