A141538 - OEIS

%I #13 Jan 12 2017 01:45:55

%S 5,5,8,7,3,9,5,7,4,7,3,7,3,0,4,6,0,4,3,9,5,2,0,9,1,2,7,6,1,7,5,0,0,4,

%T 4,9,8,2,9,0,9,0,2,0,1,0,6,2,4,5,4,5,4,8,2,1,2,7,0,7,1,8,2,0,5,6,4,9,

%U 7,0,2,9,5,3,1,4,9,2,6,1,0,1,2,2,8,6,6,0,3,0,4,2,1,9,1,2,3,1,6,3,5,7,4,1,5

%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

%e 0.55873957473730460439520912761750044982909020106245454821270718205...

%p print((7*sqrt(2)+4+3*log(1+sqrt(2)))/(3*Pi^2)) ; # _R. J. Mathar_, Aug 20 2008

%t RealDigits[(7 Sqrt[2] + 4 + 3*Log[1 + Sqrt@2])/(3*Pi^2), 10, 111][[1]] (* _Robert G. Wilson v_ *)

%K cons,easy,nonn

%O 0,1

%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