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.
Since we're aiming at data-driven applications, we'll be implementing some of these ideas in code, not just on pencil and paper. Towards the end of the course, you'll write code blocks and encounter Jupyter notebooks in Python, but don't worry, these will be quite short, focussed on the concepts, and will guide you through if you’ve not coded before.
At the end of this course you will have an intuitive understanding of vectors and matrices that will help you bridge the gap into linear algebra problems, and how to apply these concepts to machine learning.
本课程是 Mathematics for Machine Learning 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
4.6
1,565 个评分
您将获得的技能
Eigenvalues And EigenvectorsBasis (Linear Algebra)Transformation MatrixLinear Algebra
教学大纲 - 您将从这门课程中学到什么
周
1Introduction 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 个视频（共 31 分钟）, 4 个阅读材料, 3 个测验
5 个视频
Motivations for linear algebra3分钟
Getting a handle on vectors9分钟
Operations with vectors11分钟
Summary1分钟
4 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
3 个练习
Solving some simultaneous equations15分钟
Exploring parameter space20分钟
Doing some vector operations12分钟
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2Vectors 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 个视频（共 44 分钟）, 4 个测验
8 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
4 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
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3Matrices 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 个视频（共 58 分钟）, 3 个测验
8 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
2 个练习
Using matrices to make transformations12分钟
Solving linear equations using the inverse matrix16分钟
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4Matrices 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 个视频（共 56 分钟）, 4 个测验
6 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
2 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20%
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创建者 CS•Apr 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 PL•Aug 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
David Dye
Professor of MetallurgyDepartment of Materials
Samuel J. Cooper
LecturerDyson School of Design Engineering
A. Freddie Page
Strategic Teaching FellowDyson 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.
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