行列式的计算方法探讨

Research on the Computing Methods of Determinant

行列式计算的技巧性很强。理论上,任何一个行列式都可以按照定义进行计算,但是直接按照定义计算而不借助于计算机有时是不可能的。本文在总结已有常规行列式计算方法的基础上,结合历年数学专业硕士研究生入学考试试题特征性进行分析,对行列式的计算方法和一些技巧进行了更深入的探讨。总结出"定义法"、"化三角形法"、"用行列式的性质转化为已知的行列式"、"滚动消去法"、"拆分法"、"加边法"、"归纳法"、"利用递推降级法"、"利用重要的结论与重要公式"、"特征值法"等10种计算技巧和途径。

The computing methods of determinant rely much on techniques. Theoretically, each determinant can be computed by the definition of determinant. However, it is sometimes impossible to indirectly compute by the definition, rather than by computer. Therefore, it is very necessary and meaningful to discuss the computing methods of determinant. Based on the computing methods of the determinant and the analysis of test questions＇ characteristics for higher algebra in master graduate entrance exam, in this paper, I futher study and discuss some computing methods and skills of the determinant. Theremore, I summarize ten methods and skills as following ： the method by definition, transforming triangular determinant, transforming the known determinant, rolling elimination technique, splitting method, bordering determinant, induction method, recursiving relegation method, the important conclusions and formulas, and eigenvalue method.