determinant

determinant的音标是[dɪˈtɜːmɪnənt]，基本翻译是“决定因素；[数] 矩阵因子；[数] 特征值”。

速记技巧：可以尝试使用谐音法来记忆，可以将determinant的发音音译为“德西梦乃恩”，这样便于记忆。具体来说，可以将“德”理解为“determinate”，表示确定的；“西”可以联想到“size”大小；“梦”可以联想到“momentum”动量；“乃”可以联想到“natural number”自然数；“恩”可以联想到“entity”实体。这样，通过谐音联想，可以更加快速和容易地记住该单词的含义。

Determinant 的词源：

词根：determinant

词源：拉丁语 deterrere，意为“驱赶”

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 (adj.) - 决定性的，明确的

2. Determinate number (n.) - 确切的数字，确定的数量

3. Determinate process (n.) - 决定性的过程

4. Determinate sentence (n.) - 有确定结果的判决

5. Determinate function (n.) - 确定函数，有明确定义的函数

6. Determinate equation (n.) - 有确定解的方程

7. Determinate matrix (n.) - 确定矩阵，有明确特征值的矩阵

8. Determining factor (n.) - 决定因素，关键因素

9. Determining influence (n.) - 决定性影响，关键性作用

10. Determinism (n.) - 决定论，认为一切由自然法则或因果关系决定的理论

Determinant 作为名词时，意为“决定因素，关键因素”。在数学中，行列式（determinant）这个词也与 determinant 相关，表示一个矩阵中所有元素对于其他元素的乘积的代数符号。这个词的引入是为了解决线性代数中关于矩阵性质的问题。

常用短语：

1. determinant of a matrix

2. determinant of a system of equations

3. absolute determinant

4. sign of a determinant

5. determinant of a square matrix

6. determinant of a polynomial

7. determinant of a vector space

双语句子：

1. The determinant of a matrix is equal to the product of the rows.

2. The determinant of a system of equations determines the solution set.

3. The absolute value of the determinant is equal to the product of the rows multiplied by the sign of the determinant.

4. Determinants are important in linear algebra because they can be used to solve systems of equations efficiently.

5. The determinant of a square matrix is a number that determines the symmetry and stability of a system of equations.

6. Determinants are also used in polynomial equations to find the roots and coefficients.

7. Determinants are an essential part of vector spaces and linear transformations.

英文小作文：

Determinants are an essential part of mathematics and mathematical physics, particularly in linear algebra and differential equations. They can be used to solve systems of equations efficiently and are also important in understanding the symmetry and stability of mathematical systems. Determinants can also be used to find roots and coefficients in polynomial equations, and they are an essential part of vector spaces and linear transformations. Determinants are also closely related to the concept of a characteristic polynomial, which plays an important role in the study of linear differential equations. In summary, determinants are an incredibly useful tool in mathematics and mathematical physics, and they provide a powerful way of understanding and solving complex mathematical problems.