Quaternion Matrix

Quaternion matrices, extensions of complex matrices using quaternion numbers, are being actively researched for their ability to efficiently represent and process multi-dimensional data, particularly in image and signal processing. Current research focuses on developing quaternion-based algorithms for tasks like image inpainting, matrix factorization, and spectral analysis of graphs, often employing techniques such as tensor ring decompositions, quaternion Fourier transforms, and novel power methods for eigenvalue computation. These advancements offer improved performance in various applications, including color image processing, computer vision (e.g., pose estimation and background modeling), and machine learning, by leveraging the inherent advantages of quaternions in handling multi-channel data and rotational information.