Abstract
Matrices where all minors are nonnegative are said to be totally nonnegative (TN) matrices. In the case of banded TN matrices, which can be expressed by products of several bidiagonal TN matrices, Fukuda et al. (Annal. Mat. Pura Appl. 192, 423---445, 2013) discussed the eigenvalue problem from the viewpoint of the discrete hungry Toda (dhToda) equation. The dhToda equation is a discrete integrable system associated with box and ball systems. In this paper, we consider an inverse eigenvalue problem for such banded TN matrices by examining the properties of the dhToda equation. This problem is a real-valued nonnegative inverse eigenvalue problem. First, we show the determinant solution to the dhToda equation with suitable boundary conditions. Next, we clarify the relationship between the characteristic polynomials of the banded TN matrices and the determinant solution. Finally, taking this relationship into account, we design a finite-step procedure for constructing banded TN matrices with specified eigenvalues. We also present an example to demonstrate this procedure.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
