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On the inverse eigenvalue problem for nonnegative matrices of order two to five. (English) Zbl 1241.15008
This paper provides, under some particular conditions, solutions for the inverse eigenvalue problem for nonnegative matrices up to order 5.
15A18Eigenvalues, singular values, and eigenvectors
15A29Inverse problems in matrix theory
Full Text: DOI
[1] T.J. Laffey, Helena, S˘migoc, On a Classic Example in the Nonnegative Inverse Eigenvalue Problem, vol. 17, ELA, July 2008, pp. 333 -- 342.
[2] S&breve, Helena; Migoc: The inverse eigenvalue problem for nonnegative matrices, Linear algebra appl. 393, 365-374 (2004)
[3] Lowey, R.; London, D.: A note on an inverse problem for nonnegative matrices, Linear and multilinear algebra 6, 83-90 (1978) · Zbl 0376.15006 · doi:10.1080/03081087808817226
[4] Reams, R.: An inequality for nonnegative matrices and the inverse eigenvalue problem, Linear and multilinear algebra 41, 367-375 (1996) · Zbl 0887.15015 · doi:10.1080/03081089608818485
[5] Laffey, T. J.; Meehan, E.: A characterization of trace zero nonnegative $5\times 5$ matrices, Linear algebra appl. 302 -- 303, 295-302 (1999) · Zbl 0946.15008 · doi:10.1016/S0024-3795(99)00099-3
[6] Ikramov, Kh.D.; Chugunov, V. N.: Inverse matrix eigenvalue problems, J. math. Sci. 98, No. 1, 51-136 (2000) · Zbl 0954.65032 · doi:10.1007/BF02355380
[7] Suleimanova, K. R.: Stochastic matrices with real characteristic values, Dokl. akad. Nauk. SSSR 66, 343-345 (1949) · Zbl 0035.20903
[8] Johnson, C. R.: Row stochastic matrices similar to doubly stochastic matrices, Linear and multilinear algebra 10, No. 2, 113-130 (1981) · Zbl 0455.15019 · doi:10.1080/03081088108817402
[9] Friedland, S.: On an inverse problem for nonnegative and eventually nonnegative matrices, Israel J. Math. 29, No. 1, 43-60 (1978) · Zbl 0407.15015 · doi:10.1007/BF02760401
[10] S&breve, Helena; Migoc: Construction of nonnegative matrices and the inverse eigenvalue problem, Linear and multilinear algebra 53, No. 2, 85-96 (2005)
[11] Torre-Mayo, J.; Abril-Raymundo, M. R.; Alarcia-Estevez, E.; Marijuan, C.; Pisonero, M.: The nonnegative inverse eigenvalue problem from the coefficients of the characteristic polynomial. EBL digraphs, Linear algebra appl. 426, 729-773 (2007) · Zbl 1136.15007 · doi:10.1016/j.laa.2007.06.014
[12] Eleanor Meehan, Some Results On Matrix Spectra, Ph.D. Thesis, University College Dublin, 1998. · Zbl 0907.15013
[13] Rojo, Oscar; Soto, Ricardo L.: Existence and construction of nonnegative matrices with complex spectrum, Linear algebra appl. 368, 53-69 (2003) · Zbl 1031.15017 · doi:10.1016/S0024-3795(02)00650-X