ABSTRACT In this paper, we investigate the theories, properties, and applications related to the eigenvalues belonging to the th‐order quaternion tensor via T‐product, namely the th‐order T‐eigenvalue. To begin with, we present the definition of higher‐order block tensors over quaternions. Next, we introduce the th‐order T‐eigenvalue of tensors under quaternion domain and outline an algorithm for calculating the right th‐order T‐eigenvalues with their associated eigentensors by utilizing the complex representation tensor of the th‐order quaternion tensor, along with an example. Moreover, we explore the application of th‐order T‐eigenvalues in color video compression and compare our method to several existing techniques. Under the same conditions, our method consistently demonstrates lower relative errors and less CPU time than other algorithms, and the average PSNR and SSIM values are higher than those of other methods, indicating that our video compression method is better. Lastly, we consider the application of color facial recognition, and we compare our method with some state‐of‐art methods used for color facial recognition, where a higher recognition rate and less CPU time indicate the potential advantages of our approach.
Deng et al. (Wed,) studied this question.