Jacobi formula中文一般译成什么？

wufaxian

假设 A 是 5x5 矩阵，它的行 1 的单元乘来自行 2-5 的行列式(余子式)得到行列式。“雅克比公式”把来自行 1 与 2 的 2x2 行列式，乘上来自行 3-5 的 3x3行列式得到 det A。你能猜想“雅克比公式”吗？

答案：The cofactor formula adds 1 by 1 determinants (which are just entries) times their cofactors of size n&#8722;1. Jacobi discovered that this formula can be generalized. For n = 5, Jacobi multiplied each 2 by 2 determinant from rows 1-2 (with columns a < b) times a 3 by 3 determinant from rows 3-5 (using the remaining columns c < d < e). The key question is + or &#8722; sign (as for cofactors). The product is given a + sign when a, b, c, d, e is an even permutation of 1, 2, 3, 4, 5. This gives the correct determinant +1 for that permutation matrix. More than that, all other P that permute a, b and separately c, d, e will come out with the correct sign when the 2 by 2 determinant for columns a, b multiplies the 3 by 3 determinant for columns c, d, e.


以上有两个问题，

Jacobi formula中文一般译成什么？按文中的译名“ 雅克比公式”在网上搜不到有用信息。

1-2行2x2的行列式的计算结果如何与3-5行行列式的结果配对相乘？

这样计算的计算量比常规求行列式的计算量少么？如果计算量没变换，那么这样做的目的是？或者像分块矩阵乘法那样是为了解决计算机内存不够的一种方法？

anyon

我怎么看这个描述越看越像拉普拉斯定理呢