householder

Householder 的音标是["haʊʃəʊHolder]，基本翻译为“豪斯霍尔德”。速记技巧可以考虑将每个音节尽量缩短，如“豪-书-豪-尔”，这样可以方便记忆。

Householder的英文词源为：

"House" - 指房子，房间，通常与"holder"一起使用，表示持有者或拥有者。

"Holder" - 指持有某物的人，通常用于描述数学中的矩阵变换。

Householder的相关变化形式包括复数形式"Householders"，过去式"Householdsed"和过去分词"Householded"。

相关单词：

1. "Household" - 指家庭，通常用于描述一个家庭或家庭成员。

2. "Household items" - 指家庭用品或日常用品。

3. "Household budget" - 指家庭预算，用于管理家庭财务。

4. "Household income" - 指家庭收入，通常用于描述家庭成员的总收入。

5. "Household appliances" - 指家用电器，如电视、冰箱、洗衣机等。

6. "Household goods" - 指家庭财产或个人物品。

7. "Householder transformation" - 指一种矩阵变换方法，用于优化矩阵运算。

8. "Householder vector" - 指一种特殊的向量，用于描述矩阵变换的性质。

9. "Household management" - 指家庭管理或财务管理，通常用于描述家庭成员如何管理家庭财务。

10. "Household income tax" - 指家庭所得税，用于描述政府对家庭收入征收的税收。

以上这些单词都与Householder有着密切的联系，并且可以用来描述与家庭、财务管理、矩阵变换等相关的概念。

常用短语：

1. householder transformation

2. householder vectors

3. householder reflection

4. householder matrix

5. householder transformation matrix

6. householder transformation coefficients

7. householder transformation matrix inverse

双语句子：

1. 在执行矩阵变换时，我们经常使用Householder变换。

2. 矩阵的Householder变换可以有效地降低维度。

3. 如果你想找到一个矩阵的特征向量，你可以使用Householder变换。

4. 在优化问题中，Householder变换是一种常用的方法。

5. 如果你想在计算机视觉中处理图像，Householder变换是一个有用的工具。

6. 使用Householder变换，我们可以轻松地找到矩阵的奇异值。

7. 在线性代数中，Householder变换是一种重要的技术。

英文小作文：

Title: Householder Transformation in Linear Algebra

Linear algebra is a fundamental topic in mathematics that deals with vectors and matrices. One of the most powerful techniques in linear algebra is the Householder transformation, which is a method used to reduce the dimensionality of a matrix or find its eigenvectors and singular values.

In practical applications, Householder transformation is used in various fields such as matrix manipulation in computer science, optimization problems in engineering, and computer vision for image processing. It is also used in linear regression, principal component analysis, and other statistical methods.

Through Householder transformation, we can easily find the eigenvectors of a matrix, which are the most important characteristics of a matrix that determine its behavior. Additionally, it allows us to construct reflection matrices that can be used for various purposes, such as improving the conditioning of a system or reducing the effects of noise in images.

In summary, Householder transformation is a powerful tool in linear algebra that can be used to solve various problems in different fields. It provides a simple and effective way to manipulate matrices and discover their hidden characteristics.