In this paper, we investigate the eigenvalues of quaternion tensors under Einstein Product and their applications in color video processing. We present the Ger\(\check{s}\)gorin theorem for quaternion tensors. Furthermore, we have executed some experiments to validate the efficacy of our proposed theoretical framework and algorithms. Finally, we contemplate the application of this methodology in color video compression, in which the reconstruction of an approximate original image is achieved by computing a limited number of the largest eigenvalues, yielding a favorable outcome. In summary, by utilizing block tensors in its iterations, this method converges more rapidly to the desired eigenvalues and eigentensors, which significantly reduces the time required for videos compression.

在本文中，我们研究了爱因斯坦积下四元数张量的特征值及其在彩色视频处理中的应用。我们提出了四元数张量的 Ger\（\check{s}\）gorin 定理。此外，我们还进行了一些实验来验证我们提出的理论框架和算法的有效性。最后，我们考虑了这种方法在彩色视频压缩中的应用，其中通过计算有限数量的最大特征值来实现近似原始图像的重建，从而产生有利的结果。总之，通过在迭代中使用块张量，这种方法可以更快地收敛到所需的特征值和特征张量，从而显著减少视频压缩所需的时间。