2008/08/14 by Greg Martin, Martin, Greg, Erick B. Wong +1
Mathematics · #15A18 #15A36 #15A52 (Primary) 11C20 #60C05 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR) #math.NT #math.PR #msc:11C20 #msc:15A18 #msc:15A36 #msc:15A52 #msc:60C05
paper · pdf · doi:10.48550/arxiv.0808.1922
18 pages, 2 figures
arxiv created 2008/08/14 · arxiv updated 2009/12/01
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.