A complex structure-preserving algorithm for the full rank decomposition of quaternion matrices and its applications

• Published in: Numerical algorithms Vol. 91; no. 4; pp. 1461 - 1481
• Main Authors: Wang, Gang, Zhang, Dong, Vasiliev, Vasily. I., Jiang, Tongsong
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2022; Springer Nature B.V
• Subjects: Algebra; Algorithms; Color imagery; Computer Science; Decomposition; Image classification; Linear equations; Numeric Computing; Numerical Analysis; Original Paper; Quaternions; Theory of Computation; Complex structure-preserving algorithm; Full rank decomposition; Quaternion matrix; Sparse representation classification; 15A33; Complex representation
• ISSN: 1017-1398; 1572-9265
• DOI: 10.1007/s11075-022-01310-1

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.