THE HOFFMAN–WIELANDT INEQUALITY FOR QUATERNION MATRICES AND QUATERNION MATRIX POLYNOMIALS
Document Type
Article
Publication Title
Mathematical Inequalities and Applications
Abstract
The purpose of this paper is to derive the Hoffman-Wielandt inequality and its generalization for quaternion matrices. Diagonalizability of the block companion matrix of certain quadratic (linear) quaternion matrix polynomials is brought out. As a consequence, we prove that if Q(l) is another quadratic (linear) quaternion matrix polynomial, then under certain conditions on the coefficients, a generalization of the Hoffman-Wielandt inequality for their corresponding block companion matrices holds. We also prove that if P(l) is a quaternion matrix polynomial with unitary coefficients, then any right eigenvalue l0 of P(l) lies in the annular region 1 2< |l0| < 2.
First Page
609
Last Page
622
DOI
10.7153/mia-2025-28-37
Publication Date
10-1-2025
Recommended Citation
Basavaraju, Pallavi; Hadimani, Shrinath; and Jayaraman, Sachindranath, "THE HOFFMAN–WIELANDT INEQUALITY FOR QUATERNION MATRICES AND QUATERNION MATRIX POLYNOMIALS" (2025). Open Access archive. 12500.
https://impressions.manipal.edu/open-access-archive/12500
