Abstract

What is the probability that an integer matrix chosen at random has a particular integer as an eigenvalue, or an integer eigenvalue at all? For a random real matrix, what is the probability of there being a real eigenvalue in a particular interval? This paper solves these questions for 2 × 2 matrices, after specifying the probability distribution suitably.

Keywords

random matrix, eigenvalue, integer eigenvalue, integer matrix, distribution of eigenvalues

Mathematical Subject Classification

Primary: 15A36, 15A52

Secondary: 11C20, 15A18, 60C05

Authors