关于行列式计算的另类降阶法  

An Alternative Reduction Method on Computing the Determinants

作　　者：邓勇[1] 

机构地区：[1]喀什师范学院数学系,新疆喀什市844006

出　　处：《大学数学》2012年第6期102-108,共7页College Mathematics

基　　金：新疆维吾尔自治区高校科研计划重点项目(XJEDU2008I31)

摘　　要：由于二阶行列式的计算仅须求两对角线元素的乘积之差,所以计算非常简单.一般地,对高阶行列式求值,虽然可用Laplace展开公式或Gauss消去法,但是展开式会非常繁杂或计算量会很大.本文利用降阶原理,得到一种只需计算二阶行列式就可求出n(n≥3)阶方阵行列式值的另类方法.Because of the determinant of 2-by-2 matrix evaluation is the product of entries on the main diagonal minus the product of the other entries. Thus 2-by-2 determinant can usually be computed very simply. In general, any determinant can be calculated from the formula of Laplace expansion or elimination method of Gauss, but this involves formidable amounts of arithmetic if the dimension is at all large. In this paper, an alternative reduction method to compute the determinants of n（n ≥3） matrices by reducing their orders is given, which only involves the calculation of 2-by-2 determinant.

关 键 词：行列式 计算 降阶 Laplace展开法 高斯消去法 

分 类 号：O151.21[理学—数学]