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

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Abstract

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.

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Funding

This paper is supported by the Shandong Natural Science Foundation (No. ZR201709250116) and Chinese Government Scholarship (CSC No. 202008370340, No. 202108370086).

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Correspondence to Vasily. I. Vasiliev or Tongsong Jiang.

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The authors declare no competing interests.

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Wang, G., Zhang, D., Vasiliev, V.I. et al. A complex structure-preserving algorithm for the full rank decomposition of quaternion matrices and its applications. Numer Algor 91, 1461–1481 (2022). https://doi.org/10.1007/s11075-022-01310-1

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  • DOI: https://doi.org/10.1007/s11075-022-01310-1

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