27th Conference of the International Linear Algebra Society (ILAS 2026)

T-Eigenvalues of Third-order Quaternion Tensors

May 19, 2026, 2:50 PM

25m

Goodwin Hall 145

Minisymposium Talk Matrix Inequalities, Matrix Equations, and Their Applications Matrix Inequalities, Matrix Equations, and Their Applications

Speaker

Meiling Deng (University of Nevada, Reno)

Description

In this talk, we investigate the eigenvalue problem for third-order quaternionic tensors. We first introduce the notion of right T-eigenvalues and develop an efficient algorithm for their computation, whose effectiveness is demonstrated through comparative numerical experiments.

For Hermitian quaternionic tensors, we then derive bounds for the eigenvalues of tensor sums and extend Weyl’s classical theorem from matrices to the tensor setting.

Finally, we generalize the Ger\v{s}gorin disc theorem to obtain eigenvalue localization results for such tensors, providing a practical tool for spectral estimation.