Inverse eigenvalue problem of interval nonnegative matrices via lower triangular matrices

Subject Areas : Linear and multilinear algebra; matrix theory

A. M.  Nazari ¹ (Department of Mathematics, Arak University, P.O. Box 38156-8-8349, Arak, Iran)
M.  Zeinali ² (Department of Mathematics, Shahid Rajaee University, Lavizan, Tehran, Iran)
H.  Mesgarani ³ (Department of Mathematics, Shahid Rajaee University, Lavizan, Tehran, Iran)
A.  Nezami ⁴ (Department of Mathematics, Arak University, P.O. Box 38156-8-8349, Arak, Iran)

Received: 2023-11-08 Accepted : 2024-01-15 Published : 2024-02-14

Keywords: Interval matrix‎, ‎interval arithmetics‎, ‎inverse eigenvalue problem‎, ‎nonnegative matrices,

Abstract :

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.

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