Research on the Application of Laplace's Theorem in the Calculation of Determinants
Journal: Region - Educational Research and Reviews DOI: 10.32629/rerr.v6i10.2720
Abstract
As an important part of algebra, determinant can be used to judge the solution of linear equations, calculate the dimension of vector space, judge the reversibility of square matrices, etc., but its calculation is often difficult to solve. This paper first introduces Laplace's theorem and its inferences, and gives the proof process. After that, the process of solving problems with Laplace's theorem is summarized, some ideas are obtained, and the feasibility and applicability of ideas are proved by examples.
Keywords
determinant, algebra, Laplace's theorem, idea, feasibility and applicability
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[2] Wan Mingzhu. On the Expansion of Determinants of Order (n ≥ 2) - A Proof of Laplace's Theorem [J]. Journal of Anshan Normal University. 1988; (4): 1-3+14.
[3] Feng Yihu, Yang Xingxing. Application of Laplace's theorem in determinant calculation [J]. Journal of Xinzhou Normal University. 2021; 37(2): 14-17.
[4] A new proof of Laplace's theorem [J]. Journal of chifeng institute (natural science edition). 2012; 28(09): 6-7.
[5] Peng Xuemei. Simplified proof of Laplace's theorem [J]. Mathematical Bulletin. 1993; (12): 37-38.
[6] Ma Jiaqi. Using Laplace's Theorem to Calculate Determinants [J]. Mathematical Learning and Research. 2019; (19): 4.
[7] Huang Chengxing, Wang Zhimin. Calculation methods for a type of determinant [J]. Science and Technology Wind. 2023; (35): 105-107.
[8] Yu Meihua. Calculation Method for Determinants [J]. Modern Vocational Education. 2022; (44): 17-19.
[9] Liu Jiang'an, Zhu Xiaoyan, Zhou Xiaoxue, Yao Shuxia. Calculation of Determinants [J]. Science and Technology Wind. 2021; (12): 41-42.
[10] Liu Yuhan, Chen Yuxi, Chen Jiayi, Chen Bojun, Cao Xuan, Zhang Zhihan. Research on the Calculation and Proof Methods of n-order Specific Body Determinants [J]. Think Tank Era. 2023; (14): 269-272.
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