diagonal matrix

"diagonal matrix" 的音标为/daɪəˈɡæmɪtə/。

基本翻译为"对角矩阵"。这是一种特殊的矩阵，其特征值都在主对角线上。

速记技巧可以使用首字母来代替，如 DGM，这样可以快速记忆。同时，也可以使用一些记忆法，如"diagonal matrix is like a diagonal ruler（对角矩阵就像对角线上的直尺）"，这样可以更直观地记住这个概念。

Diagonal matrix的英文词源：

Diagonal matrix这个词源于希腊语中的dia-（意为“穿过”）和angle（意为“角度”）组成的词，表示矩阵中元素的位置特点。

变化形式：复数形式为diagonal matrices，过去式为diagonalized，现在分词为diagonalizing。

相关单词：

1. Diagonally - 以对角线为轴心进行旋转或平移。

2. Diagonally coupled - 对角线连接的，表示两个元素之间通过一条对角线相连的关系。

3. Diagonalization - 对角化，将矩阵转化为对角矩阵的过程。

4. Diagonally dominant - 对角线占优的，表示矩阵的对角线元素大于其他元素之和的性质。

5. Diagonalizable - 可对角化的，表示矩阵可以被分解为对角矩阵的形式。

6. Diagonally complement - 对角线补充，指在对角矩阵中添加额外的元素以形成新的矩阵。

7. Diagonal matrix element - 对角矩阵元素，表示对角矩阵中的单个元素。

8. Diagonal matrix operator - 对角矩阵算子，表示一个作用于向量上的对角矩阵。

9. Diagonalization algorithm - 对角化算法，用于将矩阵转化为对角矩阵的算法。

10. Diagonalization method - 对角化方法，是一种数学方法，用于解决某些特定类型的问题。

常用短语：

1. diagonal matrix operation

2. diagonal matrix multiplication

3. diagonal matrix inversion

4. diagonal matrix addition

5. diagonal matrix scaling

6. diagonal matrix decomposition

7. diagonal matrix exponentiation

例句：

1. The operation of multiplying a matrix by a diagonal matrix is called diagonal matrix multiplication.

2. To invert a diagonal matrix, you simply need to find its inverse.

3. Adding two diagonal matrices is equivalent to adding their corresponding elements.

4. Scaling a diagonal matrix involves multiplying each element by a constant.

5. The diagonal elements of a diagonal matrix represent the eigenvalues of the matrix.

6. Decomposing a matrix into its diagonal matrices is an important step in many algorithms.

7. Exponentiating a diagonal matrix to a power is used in some numerical methods.

英文小作文：

Diagonal matrices are a fundamental concept in linear algebra, and they arise in many different contexts. They are particularly useful when dealing with eigenvectors and eigenvalues of a matrix, as they represent the characteristic values of the matrix.

In my opinion, diagonal matrices are one of the most powerful tools in linear algebra, as they provide a simple and effective way of representing and manipulating matrices. They are also very useful in numerical analysis, where they are used to solve systems of equations and to perform various other numerical operations.

In summary, diagonal matrices are an essential part of linear algebra and numerical analysis, and they provide a simple and effective way of representing and manipulating matrices. I believe that they will continue to be used widely in the future, as they are a versatile and powerful tool that can be applied to a wide range of problems.