determinants

determinants的音标是[dɪˈtɜːmɪnənts]，基本翻译为“决定因素，决定力”。

速记技巧：使用发音类似的字母或符号来记忆单词。可以将determinants拆分为“de-ter-mi-nants”，其中de-表示“决定”，ter-mi-n表示“结束”，-ant表示“……的”，所以可以理解为“决定因素”。

请注意，以上内容仅供参考，因为学习语言需要不断练习和实践。如果需要更多信息，可以请教英语老师或查阅相关书籍。

Determinants 的词源：

词根：determinant

词源：来自拉丁语 determinant，意为“决定性的”。

变化形式：

过去式：determined

过去分词：determined

现在分词：determining

复数：determinants

相关单词：

1. Determinate - 决定性的，明确的

2. Indeterminate - 不确定的，模糊的

3. Determinism - 决定论，认为一切由因果关系决定

4. Determinate Number - 决定数，确定性数

5. Determinate Equation - 决定性方程，有解的方程

6. Determinate Boundary - 决定性边界，有解的边界条件

7. Determinate Calculus - 确定论微积分

8. Determinate Projection - 确定投影

9. Determinate Solution - 确定解，有解的解

10. Determinate System - 确定系统，有解的系统

常用短语：

1. determinant of a matrix

2. determinant of a system of equations

3. sign of a determinant

4. absolute determinant

5. minor of a determinant

6. determinant of a square matrix

7. determinant of a linear transformation

双语例句：

1. The determinant of a 2x2 matrix can be found easily using the formula. （一个2x2矩阵的行列式可以通过公式很容易地求出。）

2. The determinant of a system of equations determines the solution set. （方程组的行列式决定了解集。）

3. The sign of a determinant can sometimes indicate the direction of the solution. （行列式的符号有时可以指示解的方向。）

4. The absolute value of a determinant gives the magnitude of the solution. （行列式的绝对值给出了解的幅度。）

5. Minors of a determinant can be used to solve systems of equations efficiently. （行列式的次级可以用来有效地解决方程组。）

6. Determinants are used in linear transformations to determine the eigenvectors and eigenvalues. （在线性变换中，行列式用于确定特征向量和特征值。）

7. Determinants are an essential tool in mathematical analysis and physics. （行列式是数学分析和物理学中不可或缺的工具。）

英文小作文：

Determinants are an essential tool in mathematics that help us solve equations and systems of equations efficiently. They are also used in linear transformations to determine eigenvectors and eigenvalues, which are important concepts in mathematical physics and engineering. However, determinants can be tricky to understand, especially when dealing with higher-dimensional matrices and systems of linear equations. Understanding determinants requires a careful examination of their properties and formulas, as well as an understanding of how they relate to other mathematical concepts such as vectors and matrices. Despite their complexity, determinants are an indispensable tool in many fields of mathematics and science, and they continue to fascinate mathematicians and students alike with their beauty and power.