|
Search: id:A141538
|
|
|
| A141538 |
|
Decimal expansion of constant arising in enumerating 2 X 2 integer matrices having a prescribed integer eigenvalue. |
|
+0
1
|
|
| 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, 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, 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
(list; cons; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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 2x2 matrices.
|
|
LINKS
|
Greg Martin and Erick B. Wong, The number of 2x2 integer matrices having a prescribed integer eigenvalue, Aug 14, 2008.
|
|
FORMULA
|
(7 * sqrt(2) + 4 + 3*log(1+sqrt(2)))/(3*pi^2). - Corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 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]] (* RGWv *)
|
|
CROSSREFS
|
Sequence in context: A102729 A021183 A141864 this_sequence A003861 A107623 A081287
Adjacent sequences: A141535 A141536 A141537 this_sequence A141539 A141540 A141541
|
|
KEYWORD
|
cons,easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 15 2008
|
|
EXTENSIONS
|
Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 17 2008 and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 20 2008
|
|
|
Search completed in 0.002 seconds
|
