OFFSET
0,1
COMMENTS
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.
LINKS
Greg Martin and Erick B. Wong, The number of 2x2 integer matrices having a prescribed integer eigenvalue, arXiv:0808.1922 [math.PR], Aug 14 2008.
FORMULA
(7 * sqrt(2) + 4 + 3*log(1+sqrt(2)))/(3*Pi^2). - Corrected by R. J. Mathar, Aug 20 2008
EXAMPLE
0.55873957473730460439520912761750044982909020106245454821270718205...
MAPLE
print((7*sqrt(2)+4+3*log(1+sqrt(2)))/(3*Pi^2)) ; # R. J. Mathar, Aug 20 2008
MATHEMATICA
RealDigits[(7 Sqrt[2] + 4 + 3*Log[1 + Sqrt@2])/(3*Pi^2), 10, 111][[1]] (* Robert G. Wilson v *)
CROSSREFS
KEYWORD
AUTHOR
Jonathan Vos Post, Aug 15 2008
EXTENSIONS
Extended by Robert G. Wilson v, Aug 17 2008
Extended by R. J. Mathar, Aug 20 2008
Offset corrected R. J. Mathar, Jan 26 2009
STATUS
approved