In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. Finally we look at how to use these to do fun things with datasets - like how to rotate images of faces and how to extract eigenvectors to look at how the Pagerank algorithm works.

本课程是 数学在机器学习领域的应用 专项课程 专项课程的一部分

# Mathematics for Machine Learning: Linear Algebra

提供方

## 课程信息

### 学生职业成果

## 35%

## 34%

### 您将获得的技能

### 学生职业成果

## 35%

## 34%

#### 可分享的证书

#### 100% 在线

#### 第 1 门课程（共 3 门）

#### 可灵活调整截止日期

#### 初级

#### 完成时间大约为23 小时

#### 英语（English）

## 教学大纲 - 您将从这门课程中学到什么

**完成时间为 2 小时**

## Introduction to Linear Algebra and to Mathematics for Machine Learning

In this first module we look at how linear algebra is relevant to machine learning and data science. Then we'll wind up the module with an initial introduction to vectors. Throughout, we're focussing on developing your mathematical intuition, not of crunching through algebra or doing long pen-and-paper examples. For many of these operations, there are callable functions in Python that can do the adding up - the point is to appreciate what they do and how they work so that, when things go wrong or there are special cases, you can understand why and what to do.

**完成时间为 2 小时**

**5 个视频**

**4 个阅读材料**

**3 个练习**

**完成时间为 2 小时**

## Vectors are objects that move around space

In this module, we look at operations we can do with vectors - finding the modulus (size), angle between vectors (dot or inner product) and projections of one vector onto another. We can then examine how the entries describing a vector will depend on what vectors we use to define the axes - the basis. That will then let us determine whether a proposed set of basis vectors are what's called 'linearly independent.' This will complete our examination of vectors, allowing us to move on to matrices in module 3 and then start to solve linear algebra problems.

**完成时间为 2 小时**

**8 个视频**

**4 个练习**

**完成时间为 3 小时**

## Matrices in Linear Algebra: Objects that operate on Vectors

Now that we've looked at vectors, we can turn to matrices. First we look at how to use matrices as tools to solve linear algebra problems, and as objects that transform vectors. Then we look at how to solve systems of linear equations using matrices, which will then take us on to look at inverse matrices and determinants, and to think about what the determinant really is, intuitively speaking. Finally, we'll look at cases of special matrices that mean that the determinant is zero or where the matrix isn't invertible - cases where algorithms that need to invert a matrix will fail.

**完成时间为 3 小时**

**8 个视频**

**2 个练习**

**完成时间为 7 小时**

## Matrices make linear mappings

In Module 4, we continue our discussion of matrices; first we think about how to code up matrix multiplication and matrix operations using the Einstein Summation Convention, which is a widely used notation in more advanced linear algebra courses. Then, we look at how matrices can transform a description of a vector from one basis (set of axes) to another. This will allow us to, for example, figure out how to apply a reflection to an image and manipulate images. We'll also look at how to construct a convenient basis vector set in order to do such transformations. Then, we'll write some code to do these transformations and apply this work computationally.

**完成时间为 7 小时**

**6 个视频**

**2 个练习**

### 审阅

#### 4.7

##### 来自MATHEMATICS FOR MACHINE LEARNING: LINEAR ALGEBRA的热门评论

Great way to learn about applied Linear Algebra. Should be fairly easy if you have any background with linear algebra, but looks at concepts through the scope of geometric application, which is fresh.

Amazing course, great instructors. The amount of working linear algebra knowledge you get from this single course is substantial. It has already helped solidify my learning in other ML and AI courses.

Professors teaches in so much friendly manner. This is beginner level course. Don't expect you will dive deep inside the Linear Algebra. But the foundation will become solid if you attend this course.

Excellent review of Linear Algebra even for those who have taken it at school. Handwriting of the first instructor wasn't always legible, but wasn't too bad. Second instructor's handwriting is better.

The content of the course is very relevant, and the instructors are really fun and helpful.My only suggestion is to upload revisions for each assessment, so we can understand what we are doing wrong.

Good course with nice lecturer.\n\nSome topics should be explain more in detail and have some further reading / exercise for practicing.\n\nFor overall, this course is worth the time and money spend.

Satisfactory. Most satisfactory. Actually, this course is possibly the best linear algebra MOOC class in terms of instructor teaching style and how they pick and convey the most insightful concepts.

Great content and direction. Only negative is the sometimes frustrating experience with the Jupyter Notebooks: debugging what has gone wrong is very difficult, due to a lack of good error messages.

### 提供方

#### 伦敦帝国学院

Imperial College London is a world top ten university with an international reputation for excellence in science, engineering, medicine and business. located in the heart of London. Imperial is a multidisciplinary space for education, research, translation and commercialisation, harnessing science and innovation to tackle global challenges.

## 关于 数学在机器学习领域的应用 专项课程

## 常见问题

我什么时候能够访问课程视频和作业？

注册以便获得证书后，您将有权访问所有视频、测验和编程作业（如果适用）。只有在您的班次开课之后，才可以提交和审阅同学互评作业。如果您选择在不购买的情况下浏览课程，可能无法访问某些作业。

我订阅此专项课程后会得到什么？

您注册课程后，将有权访问专项课程中的所有课程，并且会在完成课程后获得证书。您的电子课程证书将添加到您的成就页中，您可以通过该页打印您的课程证书或将其添加到您的领英档案中。如果您只想阅读和查看课程内容，可以免费旁听课程。

退款政策是如何规定的？

有助学金吗？

还有其他问题吗？请访问 学生帮助中心。