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arXiv · 0808.1922

The number of 2x2 integer matrices having a prescribed integer eigenvalue

Greg Martin·Erick B. Wong
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Abstract

Random matrices arise in many mathematical contexts, and it is natural to ask about the properties that such matrices satisfy. If we choose a matrix with integer entries at random, for example, what is the probability that it will have a particular integer as an eigenvalue, or an integer eigenvalue at all? If we choose a matrix with real entries at random, what is the probability that it will have a real eigenvalue in a particular interval? The purpose of this paper is to resolve these questions, once they are made suitably precise, in the setting of 2x2 matrices.

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Greg Martin, Erick B. Wong. 2008-08-14. The number of 2x2 integer matrices having a prescribed integer eigenvalue. https://arxiv.org/abs/0808.1922

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