determinant的音標是[d??t??m?n?nt]，基本翻譯是“決定因素；[數] 矩陣因子；[數] 特征值”。

速記技巧：可以嘗試使用諧音法來記憶，可以將determinant的發音音譯為“德西夢乃恩”，這樣便于記憶。具體來說，可以將“德”理解為“determinate”，表示確定的；“西”可以聯想到“size”大小；“夢”可以聯想到“momentum”動量；“乃”可以聯想到“natural number”自然數；“恩”可以聯想到“entity”實體。這樣，通過諧音聯想，可以更加快速和容易地記住該單詞的含義。

Determinant 的詞源：

詞根：determinant

詞源：拉丁語 deterrere，意為“驅趕”

變化形式：

過去式：determined

過去分詞：determined

現在分詞：determining

復數：determinants

相關單詞：

1. Determinate (adj.) - 決定性的，明確的

2. Determinate number (n.) - 確切的數字，確定的數量

3. Determinate process (n.) - 決定性的過程

4. Determinate sentence (n.) - 有確定結果的判決

5. Determinate function (n.) - 確定函數，有明確定義的函數

6. Determinate equation (n.) - 有確定解的方程

7. Determinate matrix (n.) - 確定矩陣，有明確特征值的矩陣

8. Determining factor (n.) - 決定因素，關鍵因素

9. Determining influence (n.) - 決定性影響，關鍵性作用

10. Determinism (n.) - 決定論，認為一切由自然法則或因果關系決定的理論

Determinant 作為名詞時，意為“決定因素，關鍵因素”。在數學中，行列式（determinant）這個詞也與 determinant 相關，表示一個矩陣中所有元素對于其他元素的乘積的代數符號。這個詞的引入是為了解決線性代數中關于矩陣性質的問題。

常用短語：

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

雙語句子：

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.