Inverse eigenvalue problem of interval nonnegative matrices via lower triangular matrices

Journal of Linear and Topological Algebra

دوره 12، شماره 04، اسفند 2023، صفحه 281-294

نوع مقاله: Review paper

شناسه دیجیتال (DOI): 10.30495/jlta.2024.2000556.1600

نویسندگان

A. M. Nazari^{* 1}؛ M. Zeinali²؛ H. Mesgarani²؛ A. Nezami¹

¹Department of Mathematics, Arak University, P.O. Box 38156-8-8349, Arak, Iran

²Department of Mathematics, Shahid Rajaee University, Lavizan, Tehran, Iran

چکیده

In this paper, for a given set of real interval numbers $\sigma$ that satisfies in special conditions, we find an interval nonnegative matrix $C^I$ such that for each point set $\delta$ of given interval spectrum $\sigma$, there exists a point matrix $C$ of $C^I$ such that $\delta$ is its spectrum. For this purpose, we use unit lower triangular matrices and especially try to use binary unit lower triangular matrices. We also study some conditions for existence solution to the problem.
 

کلیدواژه‌ها

Interval matrix‎؛ ‎interval arithmetics‎؛ ‎inverse eigenvalue problem‎؛ ‎nonnegative matrices

مراجع

[1] C. R. Johnson, Row stochastic matrices similar to doubly stochastic matrices, Linear. Multilinear. Algebra. 10 (2) (1981), 113-130.

[2] M. Hladik, Bounds on eigenvalues of real and complex interval matrices, Appl. Math. Comput. 219 (2013), 5584-5591.

[3] M. Hladik, D. Daney, E. Tsigaridasl, A filtering method for the interval eigenvalue problem, Appl. Math. Comput. 217 (2011), 5236-5242.

[4] M. Hladik, D. Daney, E. Tsigaridasl, Bounds on real eigenvalues and singular values of interval matrices, Theo. Comp. Sci. 328 (2004), 221-244.

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

[6] J. P. Merlet, Interval analysis and robotics, Trac. Adv. Robot. 66 (2011), 147-156.

[7] A. M. Nazari, A. Nezami, M. Bayat, Inverse eigenvalues problem of distance matrices via unit lower triangular matrices, Wavelets. Linear Algebra. 10 (1) (2023), 23-36.

[8] 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.

[9] A. Nazari, M. Zeinali, H. Mesgaran, Inverse eigenvalue problem of interval nonnegative matrices of order ≤ 3, J. Math. Model. 6 (2) (2018), 187-194.

[10] J. Rohn, Inverse interval matrix, SIAM J. Numer. Anal. 30 (1993), 864-870.

[11] J. Rohn, Perron vectors of an irreducible nonnegative interval matrix, Linear. Multilinear. Algebra. 54 (2006), 399-404.

[12] K. R. Suleimanova, Stochastic matrices with real characteristic values, Dokl. Akad. Nauk. 66 (1949), 343-345.

[13] L. A. Zadeh, Fuzzy sets, Infor. Control. 8 (3) (1965), 338-353.