Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版：英文原文完整保留，中文紧随对应单元；术语采用 v20260916 确认表，自动语义审校结果可追溯。

Determinants

行列式

A determinant is a square array of elements with a prescribed evaluation rule which is depicted as follows

The evaluation rule can be illustrated by a determinant of order three.

Determinants are useful in the evaluation of vector products and vector operations like the curl.
行列式是一个元素排列成方形的数组，其评估规则如下所示。该评估规则可以通过一个三阶行列式来说明。行列式在计算向量积和向量运算（如旋度）时非常有用。
 Index

Vector calculus
索引 矢量微积分
 
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Determinant Evaluation Example

行列式计算示例

For a determinant of order three the evaluation rule is

Take the elements of the top row and multiply them times the determinant of their cofactors. The cofactor is the array left when the row and column of the given top row element is eliminated. The evaluation of the determinant of the cofactor follows the same pattern until the cofactor has dimension two. At that point, it's value is the difference of the diagonal products.
对于三阶行列式，其计算规则是：取第一行的元素，将其与它们的余子式相乘。余子式是在消去该元素所在行和列后剩下的数组。对余子式的行列式计算遵循同样的规则，直到余子式变为二维时，其值为对角线乘积之差。
 Index

Vector calculus
索引 矢量微积分
 
HyperPhysics****HyperMath*****Linear Algebra
HyperPhysics **** HyperMath ***** 线性代数
R Nave
 Go Back
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