A complex structure-preserving algorithm for the full rank decomposition of quaternion matrices and its applications - Wang, Gang; Zhang, Dong; Vasiliev, Vasily. I.; Jiang, Tongsong (Numerical algorithms, 2022)
In this paper, based on the Gauss transformation of a quaternion matrix, we study the full rank decomposition of a quaternion matrix, and obtain a direct algorithm and complex structure-preserving algorithm for full rank decomposition of a quaternion matrix. In addition, we expand the application of the above two full rank decomposition algorithms and give a fast algorithm to calculate the quaternion linear equations. The numerical examples show that the complex structure-preserving algorithm is more efficient. Finally, we apply the structure-preserving algorithm of the full rank decomposition to the sparse representation classification of color images, and the classification effect is well.