Page 115 - Textos de Matemática Vol. 39

NONNEGATIVE INVERSE EIGENVALUE PROBLEM 105
systems (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979), Lecture Notes
in Math., vol. 819, Springer, Berlin, 1980, pp. 18–34.
[2] Alberto Borobia, On the nonnegative eigenvalue problem, Linear Algebra Appl. 223/224
(1995), 131–140, Special issue honoring Miroslav Fiedler and Vlastimil Pt´ak.
[3] Mike Boyle, Symbolic dynamics and matrices, Combinatorial and graph-theoretical problems in linear algebra (Minneapolis, MN, 1991), IMA Vol. Math. Appl., vol. 50,
Springer, New York, 1993, pp. 1–38.
[4] Mike Boyle and David Handelman, The spectra of nonnegative matrices via symbolic
dynamics, Ann. of Math. (2) 133 (1991), no. 2, 249–316.
[5] J. C. Butcher and P. Chartier, The effective order of singly-implicit Runge-Kutta meth-
ods, Numer. Algorithms 20 (1999), no. 4, 269–284.
[6] Miroslav Fiedler, Eigenvalues of nonnegative symmetric matrices, Linear Algebra and
Appl. 9 (1974), 119–142.
[7] Shmuel Friedland, On an inverse problem for nonnegative and eventually nonnegative
matrices, Israel J. Math. 29 (1978), no. 1, 43–60.
[8] Charles R. Johnson, Row stochastic matrices similar to doubly stochastic matrices, Lin-
ear and Multilinear Algebra 10 (1981), no. 2, 113–130.
[9] Charles R. Johnson, Thomas J. Laffey, and Raphael Loewy, The real and the symmet-
ric nonnegative inverse eigenvalue problems are different, Proc. Amer. Math. Soc. 124
(1996), no. 12, 3647–3651.
[10] Ki Hang Kim, Nicholas S. Ormes, and Fred W. Roush, The spectra of nonnegative
integer matrices via formal power series, J. Amer. Math. Soc. 13 (2000), no. 4, 773–806
(electronic).
[11] Thomas J. Laffey, Extreme nonnegative matrices, Linear Algebra Appl. 275/276 (1998),
349–357, Proceedings of the Sixth Conference of the International Linear Algebra Society
(Chemnitz, 1996).
[12] , Realizing matrices in the nonnegative inverse eigenvalue problem, Matrices
and group representations (Coimbra, 1998), Textos Mat. S´er. B, vol. 19, Univ. Coimbra,
Coimbra, 1999, pp. 21–32.
[13] Thomas J. Laffey and Eleanor Meehan, A characterization of trace zero nonnegative
5 × 5 matrices, Linear Algebra Appl. 302/303 (1999), 295–302, Special issue dedicated
to Hans Schneider (Madison, WI, 1998).
[14] Thomas J. Laffey and Helena Sˇmigoc, Construction of nonnegative symmetric matrices
with given spectrum, Submitted for publication.
[15] , Nonnegative realization of spectra having negative real parts, Linear Algebra
Appl. 416 (2006), no. 1, 148–159.
[16] R. Loewy and J. J. McDonald, The symmetric nonnegative inverse eigenvalue problem
for 5 × 5 matrices, Linear Algebra Appl. 393 (2004), 275–298.
[17] Raphael Loewy and David London, A note on an inverse problem for nonnegative ma-
trices, Linear and Multilinear Algebra 6 (1978/79), no. 1, 83–90.
[18] Hazel Perfect, On positive stochastic matrices with real characteristic roots, Proc. Cam-
bridge Philos. Soc. 48 (1952), 271–276.
[19] Helena Sˇmigoc, The inverse eigenvalue problem for nonnegative matrices, Linear Algebra
Appl. 393 (2004), 365–374.
[20] , Construction of nonnegative matrices and the inverse eigenvalue problem, Lin-
ear Multilinear Algebra 53 (2005), no. 2, 85–96.
[21] George W. Soules, Constructing symmetric nonnegative matrices, Linear and Multilin-
ear Algebra 13 (1983), no. 3, 241–251.
[22] H. R. Sule˘ımanova, Stochastic matrices with real characteristic numbers, Doklady Akad.
Nauk SSSR (N.S.) 66 (1949), 343–345.