课程信息
4.6
1,565 个评分
283 个审阅
专项课程

第 1 门课程(共 3 门),位于

100% online

100% online

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
初级

初级

完成时间(小时)

完成时间大约为22 小时

建议:5 weeks of study, 2-5 hours/week...
可选语言

英语(English)

字幕:英语(English)...

您将获得的技能

Eigenvalues And EigenvectorsBasis (Linear Algebra)Transformation MatrixLinear Algebra
专项课程

第 1 门课程(共 3 门),位于

100% online

100% online

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
初级

初级

完成时间(小时)

完成时间大约为22 小时

建议:5 weeks of study, 2-5 hours/week...
可选语言

英语(English)

字幕:英语(English)...

教学大纲 - 您将从这门课程中学到什么

1
完成时间(小时)
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....
Reading
5 个视频(共 31 分钟), 4 个阅读材料, 3 个测验
Video5 个视频
Motivations for linear algebra3分钟
Getting a handle on vectors9分钟
Operations with vectors11分钟
Summary1分钟
Reading4 个阅读材料
About Imperial College & the team5分钟
How to be successful in this course5分钟
Grading policy5分钟
Additional readings & helpful references10分钟
Quiz3 个练习
Solving some simultaneous equations15分钟
Exploring parameter space20分钟
Doing some vector operations12分钟
2
完成时间(小时)
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....
Reading
8 个视频(共 44 分钟), 4 个测验
Video8 个视频
Modulus & inner product9分钟
Cosine & dot product5分钟
Projection6分钟
Changing basis11分钟
Basis, vector space, and linear independence4分钟
Applications of changing basis3分钟
Summary1分钟
Quiz4 个练习
Dot product of vectors15分钟
Changing basis15分钟
Linear dependency of a set of vectors15分钟
Vector operations assessment15分钟
3
完成时间(小时)
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....
Reading
8 个视频(共 58 分钟), 3 个测验
Video8 个视频
How matrices transform space5分钟
Types of matrix transformation8分钟
Composition or combination of matrix transformations7分钟
Solving the apples and bananas problem: Gaussian elimination8分钟
Going from Gaussian elimination to finding the inverse matrix8分钟
Determinants and inverses12分钟
Summary分钟
Quiz2 个练习
Using matrices to make transformations12分钟
Solving linear equations using the inverse matrix16分钟
4
完成时间(小时)
完成时间为 6 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....
Reading
6 个视频(共 56 分钟), 4 个测验
Video6 个视频
Matrices changing basis11分钟
Doing a transformation in a changed basis6分钟
Orthogonal matrices8分钟
The Gram–Schmidt process6分钟
Example: Reflecting in a plane14分钟
Quiz2 个练习
Non-square matrix multiplication10分钟
Mappings to spaces with different numbers of dimensions12分钟
4.6
283 个审阅Chevron Right
职业方向

20%

完成这些课程后已开始新的职业生涯
工作福利

83%

通过此课程获得实实在在的工作福利

热门审阅

创建者 CSApr 1st 2018

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.

创建者 PLAug 26th 2018

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.

讲师

Avatar

David Dye

Professor of Metallurgy
Department of Materials
Avatar

Samuel J. Cooper

Lecturer
Dyson School of Design Engineering
Avatar

A. Freddie Page

Strategic Teaching Fellow
Dyson School of Design Engineering

关于 Imperial College London

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....

关于 Mathematics for Machine Learning 专项课程

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....
Mathematics for Machine Learning

常见问题

  • 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。

还有其他问题吗?请访问 学生帮助中心