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We give upper and lower bounds on the determinant of a perturbation of the identity matrix or, more generally, a perturbation of a nonsingular diagonal matrix.
I. Fredholm, Sur une classe d’équations fonctionelles, Acta Math. 27
1903
Earlier work this paper cites.
J. Plemelj, Zur Theorie der Fredholmschen Funktionalgleichung, Monatsh. f. Math. 15
1904
Earlier work this paper cites.
F. P. Cantelli, Intorno ad un teorema fondamentale della teoria del rischio, Bollettino Associazione Attuari Italia (1910), 1–23
1910
Earlier work this paper cites.
H. von Koch, Über das Nichtverschwinden einer Determinante nebst Bemerkungen über Systeme unendlich vieler linearer Gleichungen, Jber. Deutschen Math. Verein. 22
1913
Earlier work this paper cites.
S. Gerschgorin, Über die Abgrenzung der Eigenwerte einer Matrix, Izv. Akad. Nauk. USSR Otd. Fiz.-Mat. Nauk 6
1931
Earlier work this paper cites.
A. M. Ostrowski, Sur la détermination des bornes inférieures pour une classe des déterminants, Bull. Sci. Math. (2) 61
1937
Earlier work this paper cites.
A. M. Ostrowski, Über die Determinanten mit überwiegender Hauptdiagonale, Comment. Math. Helv. 10
1937
Earlier work this paper cites.
A. M. Ostrowski, Sur l’approximation du déterminant de Fredholm par les déterminants des systèmes d’equations linéaires, Ark. Math. Stockholm 26A
1938
Earlier work this paper cites.
I. Gelfand, Normierte Ringe, Rec. Math. [Mat. Sbornik] N. S. , 9(51)
1941
Earlier work this paper cites.
A. M. Mood, On Hotelling’s weighing problem, Ann. Math. Stat. 17
1946
Earlier work this paper cites.
J. Williamson, Determinants whose elements are 0 0 and 1 1 , Amer. Math. Monthly 53
1946
Earlier work this paper cites.
O. Taussky, A recurring theorem on determinants, The American Mathematical Monthly 56
1949
Earlier work this paper cites.
R. Oeder, Problem E 949, Amer. Math. Monthly 58
1951
Earlier work this paper cites.
G. B. Price, Bounds for determinants with dominant principal diagonal, Proc. Amer. Math. Soc. 2
1951
Cited alongside, same era.
G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities , second edition, Cambridge University Press, 1952
1952
Cited alongside, same era.
A. M. Ostrowski, Note on bounds for determinants with dominant principal diagonal, Proc. Amer. Math. Soc. 3
1952
Cited alongside, same era.
A. M. Ostrowski, Sur les déterminants à diagonale dominante, Bull. Soc. Math. Belg. (1954), 46–51. Reprinted in [ 33 , pp. 91–96]
1954
Cited alongside, same era.
T. Muir, The Theory of Determinants in the Historical Order of Development , 4 volumes, reprinted by Dover Publications, New York, 1960
1960
Cited alongside, same era.
I. C. F. Ipsen and R. Rehman, Perturbation bounds for determinants and characteristic polynomials, SIAM J. Matrix Anal. Appl. 30
2008
Later among the works it cites.
R. Bhatia and T. Jain, Higher order derivatives and perturbation bounds for determinants, Linear Alg. Appl. 431
2009
Later among the works it cites.
F. Bornemann, On the numerical evaluation of Fredholm determinants, Math. Comp. 79
2010
Later among the works it cites.
P. Cameron, Team games, 3 , http://cameroncounts.wordpress.com/2011/04/18/team-games-3/ , posted 18 April 2011
2011
Later among the works it cites.
P. Cameron, A matrix problem , http://cameroncounts.wordpress.com/2011/08/19/a-matrix-problem/ , posted 19 Aug. 2011
2011
Later among the works it cites.
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A. M. Ostrowski, Alexander Ostrowski: Collected Mathematical Papers , Vol. 1 (Determinants, Linear Algebra, Algebraic Equations), Birkhäuser, 1983
1983
Cited alongside, same era.
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis , Cambridge University Press, 1991
1991
Cited alongside, same era.
L. Elsner, Bounds for determinants of perturbed M-matrices, Lin. Alg. Appl. 257
1997
Cited alongside, same era.
V. Maz’ya and T. Shaposhnikova, Jacques Hadamard, A Universal Mathematician , History of Mathematics, Vol. 14, AMS and LMS, 1998
1998
Cited alongside, same era.
S. Georgiou, C. Koukouvinos and J. Seberry, Hadamard matrices, orthogonal designs and construction algorithms, Designs 2002: Further computational and constructive design theory , Kluwer, 2003, 133–205
2003
Cited alongside, same era.
R. S. Varga, Geršgorin and His Circles , Springer Series in Computational Mathematics, Vol. 36, 2004
2004
Cited alongside, same era.
C. J. Colbourn and J. H. Dinitz, Handbook of Combinatorial Designs , 2 2 nd edition, CRC Press, New York, 2006
2006
Cited alongside, same era.
G. W. Stewart, Fredholm, Hilbert, Schmidt: Three fundamental papers on integral equations , 2011. Available from http://www.cs.umd.edu/~stewart/FHS.pdf
2011
Later among the works it cites.
W. Li and Y. Chen, Some new two-sided bounds for determinants of diagonally dominant matrices, J. of Inequalities and Applications 2012, 2012
2012
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2013
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2013
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2014
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W. P. Orrick and B. Solomon, The Hadamard maximal determinant problem
2014
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W. D. Smith, Constructions of n × n n\times n skew-Hadamard matrices for n = 4 , 8 , 12 , … , 96 , 100 n=4,8,12,\ldots,96,100 , http://rangevoting.org/SkewHad.html , Aug.2006 (viewed 12 March 2014)
2014
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