9.1 The formula of Determinants 行列式的计算方法叫做 Cofactor Expansion。在介绍这个方法之前,我们先介绍什么是 Cofactor (代数余子式)。 假设有一个 n×n 的矩阵 A,我们之前用 aij 表示矩阵第 i 行第 j 列的元素,现在我们用 Aij 表示矩阵第 i 行第 j 列对应的余子式。Aij 表示的是将矩阵 A 移去 第...
Keep in mind that cofactor expansion is a recursive formula. For instance, the determinant of a 5×5 matrix with cofactor expansion is expressed via several 4×4 determinants. To see how to compute them, use the cofactor expansion calculator once again. Example: the determinant of a 5×5 ma...
The determinant of A is calculated from its cofactor matrix M(A) using a Laplace expansion. For example, the Laplace expansion along the first column of A is obtained by summing the product of each entry of the first column of A with its associated entry in the first column of the cofact...