数学与应用数学-行列式的解法探究论文VIP免费

行列式的解法探究摘要 行列式的计算是高等代数的重要组成部分．通过对典型的行列式计算相关例题进行归类分析，将行列式的解法归类为三个板块：行列式的一般解法、行列式的特殊解法以及特殊行列式的解法，其中一般解法分别为三角化法、特征值法、代数余子式法，特殊解法分别为加边法、拆分法、递推法、数学归纳法、函数法、打洞原理法、拉普拉斯定理法，特殊行列式分别是循环行列式、类对角形行列式、箭形行列式和范德蒙行列式．通过以上对行列式解法的归纳探究，从而在计算行列式时选择合适的解法进行计算，能够利用它们来解决数学问题．关键词 行列式 行列式的计算 拆分法 打洞原理 范德蒙行列式Research on the Solution of DeterminantAbstract The calculation of determinant is an important part of higher algebra ． By classifying and analyzing the typical examples related to determinant calculation, the determinant solutions are classified into three sections: general solutions to determinants, special solutions to determinants, and solutions of special determinants ． The general solutions are the triangulation method, the eigenvalue method, and the algebraic cofactor method． The special solutions are the edge-addition method, the split method, the recursion induction, the mathematical induction, the function method, the hole-punching principle method, the Laplace theorem method． The special determinants are the cyclic determinant, the similar diagonal determinant, the arrow determinant, and the Vandermonde determinant． Through the above induction and exploration of the determinant solution, we can choose the appropriate solution to calculate the determinant and use them to solve mathematical problems．Key words Determinant Determinant calculation Split method Hole-punching principle Vandermonde determinant目 录引言..........................................................................11 预备知识.............................................................