n階行列式的降階法

The Reductive Algorithm for Determinant of a Matrix

黃慶順 ； 李柏堅 ； 許昭興

《加馬》 35期 (2004/06) Pp. 15-19

https://doi.org/10.30173/JG.200406.0004

摘要

我們在解線性方程組時，行列式解法是一種有效而且的方法（克萊瑪法則）。而二階行列式的計算僅須求兩對角線乘積之差即可，甚至是可以利用心算求值，可是到了高階，雖然可以用公式展，可是計算式子會非常的繁雜，所以我們創新一種方法並證它能夠擁有二階好計算的優點，又能避免高階展開時的繁雜龐大算式。

關鍵字

行列式 ； 矩陣

並列摘要

Determinants are very efficient computational method to solve system of linear equations (Cramer’s rule, the determinant of 2-by-2 matrix is the product of entries on the main diagonal minus the product of the other entries. Thus 2-by-2 determinants can usually be computed mentally. In principle, any determinant can be calculated from the formula of expansion, but this involves formidable amounts of arithmetic if the dimension is at all large. We need a new method of calculation and prove it, which is similar in 2-by-2 cases and involves less arithmetic than the methods of Laplace expansion and Gaussian Elimination.

並列關鍵字

determinant ； matrix