[1]
|
A. N. Kolmogorov, “Markov Chains with Countably Many Possible States,” Bull University, Moscow, 1937, pp. 1-16.
|
[2]
|
H. Minc, “Nonnegative Matrices,” John Wiley and Sons, New York, 1988, p. 166.
|
[3]
|
K. R. Suleimanova, “Stochastic Matrices with Real Eigenvalues,” Soviet Mathematics Doklady, Vol. 66, 1949, pp. 343-345.
|
[4]
|
R. Loewy and D. London, “A Note on an Inverse Problem for Nonnega-tive Matrices,” Linear and Multilinear Algebra, Vol. 6, No. 1, 1978, pp. 83-90.
doi:10.1080/03081087808817226
|
[5]
|
M. Fiedler, “Eigen-values of Nonnegative Symmetric Matrices,” Linear Algebra Applied, Vol. 9, 1974, pp. 119-142. doi:10.1016/0024-3795(74)90031-7UUU
|
[6]
|
M. T. Chu and G. H. Golub, “Inverse Eigenvalue Problems: Theory, Algorithms, and Applications,” Oxford University, Oxford, pp. 93-122.
|
[7]
|
R. L. SoTo, “Reliability by Symmetric Nonnegative Matrices,” http://www.scielo.cl/pdf/proy/v24n1/art06.pdf.
|
[8]
|
A. Boro-bia, “On the Nonnegative Eigenvalue Problem,” Linear Alge-bra Applied, Vol. 223-224, 1995, pp. 131-140.
doi:10.1016/0024-3795(94)00343-CUUU
|
[9]
|
M. Boyle and D. Handelman, “The Spectra of Nonnegative Matrices via Sym-bolic Dynamics,” Annals of Mathematics, Vol. 133, 1991, pp. 249-316.
doi:10.2307/2944339
|
[10]
|
P. Egleston, “Nonnegative Matrices with Prescribed Spectra,” Dissertation, Central Michigan University, 2001.
|
[11]
|
C. Johnson, “Row Stochastic Matrices Similar to Doubly Stochas-tic Matrices,” Linear and Multilinear Algebra, Vol. 10, No. 2, 1981, pp. 113-130. doi:10.1080/03081088108817402
|
[12]
|
C. Johnson, T. J. Laffey and R. Loewy, “The Real and the Symmetric Nonnega-tive Inverse Eigenvalue Problems are Different,” Proceedings of the American Mathematical Society, Vol. 124, 1996, PP. 3647-3651. doi:10.1090/S0002-9939-96-03587-3
|
[13]
|
F. Karpelevich, “On the Eigenvalues of a Matrix with Nonnegative Elements,” Izv. Akad. Nauk SSSR Ser. Mat. Vol. 15, 1951, pp. 361-383.
|
[14]
|
R. B. Kellogg, “Matrices Similar to a Positive or Essentially Posi-tive Matrix,” Linear Algebra Applied, Vol. 4, No. 3, 1971, pp. 191-204. doi:10.1016/0024-3795(71)90015-2
|
[15]
|
C. Knudsen and J. J. McDonald, “A Note on THE Convexity of the Realizable set of Eigenvalues for Nonnegative Symmetric Matrices,” Electronic Journal Linear Algebra, Vol. 8, 2001, pp. 110-114.
|
[16]
|
T. Laffey, “Realizing Matrices in the Nonnegative Inverse Eigen-value Problem,” Texts in Mathematics ,Series B, University, Coimbra, 1999, pp. 21-32.
|
[17]
|
T. Laffey and E. Meehan, “A refinement of an inequality of Johnson, Loewy, and London on Nonnegative Matrices and Some Applications,” Electron Journal Linear Algebra, Vol. 3, 1998, pp. 119-128.
|
[18]
|
T. Laffey and E. Meehan, “A Characterization of Trace zero Nonnegative 5×5 Matrices,” Linear Algebra Applied, Vol. 302-303, No. 1, 1999, pp. 295-302. doi:10.1016/S0024-3795(99)00099-3
|
[19]
|
J. J. McDonald and M. Neumann, “The Soules Approach to the Inverse Eigenvalue Problem for Nonnegative Symmetric Matrices of Order n-5,” Contemporary Mathematics, Vol. 259, 2000, pp. 387-407.
|
[20]
|
L. Mirsky and H. Perfect, “Spectral Properties of Doubly Stochastic Matrices,” Mathematics and Statistics, Vol. 69 No. 1, 1965, pp. 35-57. doi:10.1007/BF01313442
|
[21]
|
H. Perfect, “Methods of Con-structing Certain Stochastic Matrices,” Duke Mathematical Journal, Vol. 20, No. 3, 1953, pp. 395-404. doi:10.1215/S0012-7094-53-02040-7
|
[22]
|
N. Radwan, “An Inverse Eigenvalue Problem for Symmetric and Normal Matri-ces,” Linear Algebra Applied, Vol. 248, No. 15, 1996, pp. 101-109.
doi:10.1016/0024-3795(95)00162-X
|
[23]
|
R. Reams, “An Ine-quality for Nonnegative Matrices and the Inverse Eigenvalue Problem,” Linear and Multilinear Algebra, Vol. 41, No. 4, 1996, pp. 367-375. doi:10.1080/03081089608818485
|
[24]
|
G. Wuwen, “Eigen-values of Nonnegative Matrices,” Linear Algebra Applied, Vol. 266, No. 15 1997, pp. 261-270. doi:10.1016/S0024-3795(96)00007-9
|
[25]
|
X. Z. Zhan, “Matrix Theory,” Academic Press, Chinese, 2008, p. 127.
|
[26]
|
P. D. Egleston and T. D. Lenker, “Sivaram K. Narayan, the Non-negative Inverse Eigenvalue Problem,” Linear Algebra and Its Applications, Vol. 379, No. 1, 2004, pp. 475-490.
|