4.6
2,424 個評分
433 個審閱

### 您將獲得的技能

Eigenvalues And EigenvectorsBasis (Linear Algebra)Transformation MatrixLinear Algebra

1

## 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....
5 個視頻 （總計 31 分鐘）, 4 個閱讀材料, 3 個測驗
5 個視頻
Motivations for linear algebra3分鐘
Getting a handle on vectors9分鐘
Operations with vectors11分鐘
Summary1分鐘
4 個閱讀材料
About Imperial College & the team5分鐘
How to be successful in this course5分鐘
3 個練習
Solving some simultaneous equations15分鐘
Exploring parameter space20分鐘
Doing some vector operations12分鐘
2

## 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....
8 個視頻 （總計 44 分鐘）, 4 個測驗
8 個視頻
Modulus & inner product9分鐘
Cosine & dot product5分鐘
Projection6分鐘
Changing basis11分鐘
Basis, vector space, and linear independence4分鐘
Applications of changing basis3分鐘
Summary1分鐘
4 個練習
Dot product of vectors15分鐘
Changing basis15分鐘
Linear dependency of a set of vectors15分鐘
Vector operations assessment15分鐘
3

## 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....
8 個視頻 （總計 58 分鐘）, 3 個測驗
8 個視頻
How matrices transform space5分鐘
Types of matrix transformation8分鐘
Composition or combination of matrix transformations7分鐘
Solving the apples and bananas problem: Gaussian elimination8分鐘
Going from Gaussian elimination to finding the inverse matrix8分鐘
Determinants and inverses12分鐘
Summary59
2 個練習
Using matrices to make transformations12分鐘
Solving linear equations using the inverse matrix16分鐘
4

## 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....
6 個視頻 （總計 56 分鐘）, 4 個測驗
6 個視頻
Matrices changing basis11分鐘
Doing a transformation in a changed basis6分鐘
Orthogonal matrices8分鐘
The Gram–Schmidt process6分鐘
Example: Reflecting in a plane14分鐘
2 個練習
Non-square matrix multiplication10分鐘
Mappings to spaces with different numbers of dimensions12分鐘
4.6
433 個審閱

## 29%

### 熱門審閱

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.

## 關於 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. Imperial students benefit from a world-leading, inclusive educational experience, rooted in the College’s world-leading research. Our online courses are designed to promote interactivity, learning and the development of core skills, through the use of cutting-edge digital technology....

## 關於 Mathematics for Machine Learning 專項課程

For a lot of higher level courses in Machine Learning and Data Science, you find you need to freshen up on the basics in mathematics - stuff you may have studied before in school or university, but which was taught in another context, or not very intuitively, such that you struggle to relate it to how it’s used in Computer Science. This specialization aims to bridge that gap, getting you up to speed in the underlying mathematics, building an intuitive understanding, and relating it to Machine Learning and Data Science. In the first course on Linear Algebra we look at what linear algebra is and how it relates to data. Then we look through what vectors and matrices are and how to work with them. The second course, Multivariate Calculus, builds on this to look at how to optimize fitting functions to get good fits to data. It starts from introductory calculus and then uses the matrices and vectors from the first course to look at data fitting. The third course, Dimensionality Reduction with Principal Component Analysis, uses the mathematics from the first two courses to compress high-dimensional data. This course is of intermediate difficulty and will require basic Python and numpy knowledge. At the end of this specialization you will have gained the prerequisite mathematical knowledge to continue your journey and take more advanced courses in machine learning.... ## 常見問題

• 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。

• 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。