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.

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## 課程信息

### 學生職業成果

## 35%

## 34%

### 您將獲得的技能

### 學生職業成果

## 35%

## 34%

#### 可分享的證書

#### 100% 在線

#### 第 1 門課程（共 3 門）

#### 可靈活調整截止日期

#### 初級

#### 完成時間大約為23 小時

#### 英語（English）

## 教學大綱 - 您將從這門課程中學到什麼

**完成時間為 2 小時**

## 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.

**完成時間為 2 小時**

**5 個視頻**

**4 個閱讀材料**

**3 個練習**

**完成時間為 2 小時**

## 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.

**完成時間為 2 小時**

**8 個視頻**

**4 個練習**

**完成時間為 3 小時**

## 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.

**完成時間為 3 小時**

**8 個視頻**

**2 個練習**

**完成時間為 7 小時**

## 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.

**完成時間為 7 小時**

**6 個視頻**

**2 個練習**

### 審閱

#### 4.7

##### 來自MATHEMATICS FOR MACHINE LEARNING: LINEAR ALGEBRA的熱門評論

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.

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.

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.

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.

Excellent course!! The Mathematics for Machine Leaning : Linear Algebra offered by the Imperial College of London it's a good step into building a strong foundation in the field of Linear Algebra.

This was a terrific course; the instructors' are passionate and knowledgeable about the course material, the assignments are engaging and relevant, and the length of the videos feels "just right".

This is the BEST course if anyone wants to learn linear algebra for machine learning. Lectures are clear and very understandable and quiz questions are great, too. Thank you for this great course.

Be careful as a beginner in coding. It might be frustrating from time to time. I have spent the majority of my timing on the coding . At the end worthwhile, but did not feel that way at that time

### 關於 伦敦帝国学院

## 關於 数学在机器学习领域的应用 專項課程

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