Numerical Range of Toeplitz Matrices over Finite Fields

Authors

Derek Thompson, Taylor University
Maddison Guillaume Baker, Taylor University
Amish Mishra, Taylor University

Document Type

Conference Proceeding

Publication Date

5-31-2019

Abstract

We characterize the kth numerical range of all n×n Toeplitz matrices with a constant main diagonal and another single, non-zero diagonal, where the matrices are over the field Zp[i], with p a prime congruent to 3 mod 4. We find that, for k ∈ Z∗, the kth numerical range is always equal to Zp[i] with the exception of the scaled identity. We also use similar techniques to discover a general connection between the 0th numerical range and the kth numerical range. Lastly, we conclude with a conjecture regarding the general numerical range of all triangular Toeplitz matrices.

Recommended Citation

Thompson, Derek; Guillaume Baker, Maddison; and Mishra, Amish, "Numerical Range of Toeplitz Matrices over Finite Fields" (2019). ACMS Conference Proceedings 2019. 18.
https://pillars.taylor.edu/acms-2019/18