We investigate the problem of almost zeros of polynomial matrices as used in system theory. It is related to the controllability and observability notion of systems as well as the determination of Macmillan degree and complexity of systems. We also present some new results on this important invariant in the light of randomness and we prove an uncertainty type relation appearing in such ensembles of operators.

中文翻译：

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几乎零和随机性的概念

我们研究了系统理论中使用的多项式矩阵几乎为零的问题。它与系统的可控性和可观察性概念以及系统的麦克米伦度和复杂性的确定有关。我们还根据随机性提出了关于这个重要不变量的一些新结果，并且我们证明了出现在这样的算子集合中的不确定性类型关系。