论文信息 - Nonnegative realization of spectra having negative real parts

Nonnegative realization of spectra having negative real parts

Abstract The nonnegative inverse eigenvalue problem (NIEP) is the problem of determining necessary and sufficient conditions for a list of complex numbers σ to be the spectrum of a nonnegative matrix. In this paper the problem is completely solved in the case when all numbers in the given list σ except for one (the Perron eigenvalue) have real parts smaller than or equal to zero.

Thomas J. Laffey | Helena Šmigoc

[1] Mike Boyle,et al. The spectra of nonnegative matrices via symbolic dynamics , 1991 .

[2] A characterization of trace zero nonnegative 5×5 matrices , 1999 .

[3] Charles R. Johnson. Row Stochastic Matrices Similar to Doubly Stochastic Matrices , 1981 .

[4] Shmuel Friedland,et al. On an inverse problem for nonnegative and eventually nonnegative matrices , 1978 .

[5] T. Laffey. Extreme nonnegative matrices , 1998 .

[6] Charles R. Johnson,et al. The real and the symmetric nonnegative inverse eigenvalue problems are different , 1996 .

[7] Sivaram K. Narayan,et al. The nonnegative inverse eigenvalue problem , 2004 .

[8] Guo Wuwen,et al. Elgenvalues of nonnegative matrices , 1997 .

[9] Helena Šmigoc,et al. The inverse eigenvalue problem for nonnegative matrices , 2004 .

[10] Alberto Borobia,et al. Negativity compensation in the nonnegative inverse eigenvalue problem , 2004 .

[11] Robert Reams,et al. An inequality for nonnegative matrices and the inverse eigenvalue problem , 1996 .

[12] Construction of nonnegative matrices and the inverse eigenvalue problem , 2005 .

[13] H. Perfect. On positive stochastic matrices with real characteristic roots , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[14] Raphael Loewy,et al. A note on an inverse problem for nonnegative matrices , 1978 .