Imperial College London
Mathematics for Machine Learning: Linear Algebra
Imperial College London

Mathematics for Machine Learning: Linear Algebra

This course is part of Mathematics for Machine Learning Specialization

Taught in English

Some content may not be translated

David Dye
Samuel J. Cooper
A. Freddie Page

Instructors: David Dye

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Course

Gain insight into a topic and learn the fundamentals

4.7

(11,947 reviews)

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91%

Beginner level
No prior experience required
18 hours (approximately)
Flexible schedule
Learn at your own pace

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Assessments

15 quizzes

Course

Gain insight into a topic and learn the fundamentals

4.7

(11,947 reviews)

|

91%

Beginner level
No prior experience required
18 hours (approximately)
Flexible schedule
Learn at your own pace

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There are 5 modules in this course

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.

What's included

5 videos4 readings3 quizzes1 discussion prompt1 plugin

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.

What's included

8 videos4 quizzes

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.

What's included

8 videos2 quizzes1 programming assignment1 ungraded lab

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.

What's included

6 videos2 quizzes2 programming assignments2 ungraded labs

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.

What's included

9 videos1 reading4 quizzes1 programming assignment1 ungraded lab2 plugins

Instructors

Instructor ratings
4.7 (2,112 ratings)
David Dye
Imperial College London
2 Courses396,334 learners
Samuel J. Cooper
Imperial College London
2 Courses396,334 learners

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