This paper is supported by the National Natural Science Foundation of China (No. 11771188), Chinese Government Scholarship (CSC No. 202008370340) and Shandong Natural Science Foundation (No. ZR201709250116).
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Matrix decompositions play a prominent role in the theoretical study and numerical calculation of split quaternion mechanics. This paper, by means of a complex representation of split quaternion matrices, introduces Gaussian elimination of split quaternion matrices, and obtains a complex structure-preserving algorithm for split quaternion matrix LDU decomposition. Numerical examples show that the complex structure-preserving algorithm is more efficient.