%N Decimal expansion of constant arising in enumerating 2 X 2 integer matrices having a prescribed integer eigenvalue.
%C Martin and Wong, Corollary 2, p. 2. 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 2 X 2 matrices.
%H Greg Martin and Erick B. Wong, <a href="http://arxiv.org/abs/0808.1922">The number of 2x2 integer matrices having a prescribed integer eigenvalue</a>, arXiv:0808.1922 [math.PR], Aug 14 2008.
%F (7 * sqrt(2) + 4 + 3*log(1+sqrt(2)))/(3*Pi^2). - Corrected by _R. J. Mathar_, Aug 20 2008
%p print((7*sqrt(2)+4+3*log(1+sqrt(2)))/(3*Pi^2)) ; # _R. J. Mathar_, Aug 20 2008
%t RealDigits[(7 Sqrt + 4 + 3*Log[1 + Sqrt@2])/(3*Pi^2), 10, 111][] (* _Robert G. Wilson v_ *)
%A _Jonathan Vos Post_, Aug 15 2008
%E Extended by _Robert G. Wilson v_, Aug 17 2008
%E Extended by _R. J. Mathar_, Aug 20 2008
%E Offset corrected _R. J. Mathar_, Jan 26 2009