行列式计算中的降阶算法研究

The Study of Reduced-order in Determinant Computation

利用矩阵分块、矩阵乘积等方法导出一系列行列式降阶定理,将高阶转化为低阶进而进行计算.该计算方法对计算某一类型的行列式特别是特征多项式时尤为方便.针对D+CA-1B和λEn-AB型的行列式,给出了相应的结论和例证.

In this paper, a series of reduced - order theories are deduced by block - matrix and product - matrix, which can be used to make the determinant change from the higher - order to lower one so as to be calculated. The method is particularly convenient to calculate a certain type determinant especially characteristic polynomial. For the determinant of │D＋CA^-1B│ and│λEn-AB│, the relevant conclusion and illustration are given in this paper.