An isospectral flow manipulates a matrix preserving its spectrum. In this paper, we study a flow, originally introduced by Arsie and Ebenbauer [2], of the form  where  is the time derivative of matrix P, P' is transpose of matrix P, and is same as matrix  on the upper triangular elements and all elements below the diagonal are zero. We extend results in [2] to the case of real banded (band) matrices. If the initial condition,   is a banded matrix having lower bandwidth p > 0 with a simple and real spectrum, then  converges as  to a banded symmetric matrix having bandwidth p, isospectral to P₀. Also, the limit point has the same sign pattern in the pth subdiagonal elements as in P₀.

isospectral flow, differential equations on manifolds, limit set, symmetric matrices, sparse matrices, banded matrices.

Received: August 10, 2022; Accepted: September 27, 2022; Published: October 13, 2022

How to cite this article: Krishna P. Pokharel, A study of isospectral flow on banded matrices, Far East Journal of Dynamical Systems 35 (2022), 7-22. http://dx.doi.org/10.17654/0972111822007

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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