課程信息
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第 1 門課程(共 3 門)

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初級

完成時間大約為21 小時

建議:5 weeks of study, 2-5 hours/week...

英語(English)

字幕:英語(English)

您將獲得的技能

Eigenvalues And EigenvectorsBasis (Linear Algebra)Transformation MatrixLinear Algebra

第 1 門課程(共 3 門)

100% 在線

立即開始,按照自己的計劃學習。

可靈活調整截止日期

根據您的日程表重置截止日期。

初級

完成時間大約為21 小時

建議:5 weeks of study, 2-5 hours/week...

英語(English)

字幕:英語(English)

教學大綱 - 您將從這門課程中學到什麼

1
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....
5 個視頻 (總計 28 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
Grading policy5分鐘
Additional readings & helpful references10分鐘
3 個練習
Exploring parameter space20分鐘
Solving some simultaneous equations15分鐘
Doing some vector operations14分鐘
2
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....
8 個視頻 (總計 44 分鐘), 4 個測驗
8 個視頻
Modulus & inner product10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
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....
8 個視頻 (總計 57 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 transformations8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 inverses10分鐘
Summary59
2 個練習
Using matrices to make transformations12分鐘
Solving linear equations using the inverse matrix16分鐘
4
完成時間為 6 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....
6 個視頻 (總計 53 分鐘), 4 個測驗
6 個視頻
Matrices changing basis11分鐘
Doing a transformation in a changed basis4分鐘
Orthogonal matrices6分鐘
The Gram–Schmidt process6分鐘
Example: Reflecting in a plane14分鐘
2 個練習
Non-square matrix multiplication20分鐘
Example: Using non-square matrices to do a projection12分鐘
5
完成時間為 4 小時

Eigenvalues and Eigenvectors: Application to Data Problems

Eigenvectors are particular vectors that are unrotated by a transformation matrix, and eigenvalues are the amount by which the eigenvectors are stretched. These special 'eigen-things' are very useful in linear algebra and will let us examine Google's famous PageRank algorithm for presenting web search results. Then we'll apply this in code, which will wrap up the course....
9 個視頻 (總計 44 分鐘), 1 個閱讀材料, 5 個測驗
9 個視頻
What are eigenvalues and eigenvectors?4分鐘
Special eigen-cases3分鐘
Calculating eigenvectors10分鐘
Changing to the eigenbasis5分鐘
Eigenbasis example7分鐘
Introduction to PageRank8分鐘
Summary1分鐘
Wrap up of this linear algebra course1分鐘
1 個閱讀材料
Did you like the course? Let us know!10分鐘
4 個練習
Selecting eigenvectors by inspection20分鐘
Characteristic polynomials, eigenvalues and eigenvectors30分鐘
Diagonalisation and applications20分鐘
Eigenvalues and eigenvectors25分鐘
4.7
490 個審閱Chevron Right

31%

完成這些課程後已開始新的職業生涯

30%

通過此課程獲得實實在在的工作福利

熱門審閱

創建者 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.

創建者 NSDec 23rd 2018

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.

講師

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David Dye

Professor of Metallurgy
Department of Materials
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Samuel J. Cooper

Lecturer
Dyson School of Design Engineering
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A. Freddie Page

Strategic Teaching Fellow
Dyson School of Design Engineering

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....
Mathematics for Machine Learning

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