On the nonnegative inverse eigenvalue problem of traditional matrices

محورهای موضوعی : Linear and multilinear algebra; matrix theory

A. M. Nazari ¹ (Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran)
S. Kamali Maher ² (Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran)

تاریخ دریافت : 1391/10/12 تاریخ پذیرش : 1391/10/12 تاریخ انتشار : 1392/06/10

کلید واژه: Inverse eigenvalue problem, Tridiagonal matrix, Nonnegative matrix,

چکیده مقاله :

In this paper, at first for a given set of real or complex numbers $\sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $\sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.

منابع و مأخذ:

[1] T. J. Laey, Helena. Smigoc, On a Classic Example in the Nonnegative Inverse Eigenvalue Problem, vol. 17, ELA, July 2008, pp. 333-342.

[2] R. Lowey, D. London, A note on an inverse problem for nonnegative matrices, Linear and Multilinear Algebra 6 (1978) 83-90.

[3] Helena Smigoc, The inverse eigenvalue problem for nonnegative matrices, Linear Algebra Appl. 393 (2004) 365-374.

[4] T. J. Laey, E. Meehan, A characterization of trace zero nonnegative 55matrices, Linear Algebra Appl. 302-303 (1999) 295-302.

[5] A. M. Nazari, F. Sherafat, On the inverse eigenvalue problem for nonnegative matrices of order two to five, Linear Algebra Appl. 436 (2012) 1771-1790.

[6] C. R. Johnson, Rowstochastic matrices similar to doubly stochasticmatrices, Linear and MultilinearAlgebra 10 (2) (1981) 113-130.

[7] M. T. Chu, G. H. Golub, Inverse Eigenvalue Problems: Theory, Algorithms and Applications, Oxford University Press, New York, 2005.

[8] H. Hochstadt, On the construction of a Jacobi matrix from mixed given data, Linear Algebra Appl. 28 (1979) 113-115.

[9] H. Pickmann, R. L. Soto, J. Egana, M. Salas, An inverse eigenvalue problem for symmetrical tridiagonal matrices, Computers and Mathematics with Applications 54 (2007) 699-708.