About this Course
4.6
1,627 ratings
291 reviews
Specialization
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100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Beginner Level

Beginner Level

Hours to complete

Approx. 22 hours to complete

Suggested: 5 weeks of study, 2-5 hours/week...
Available languages

English

Subtitles: English...

Skills you will gain

Eigenvalues And EigenvectorsBasis (Linear Algebra)Transformation MatrixLinear Algebra
Specialization
100% online

100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Beginner Level

Beginner Level

Hours to complete

Approx. 22 hours to complete

Suggested: 5 weeks of study, 2-5 hours/week...
Available languages

English

Subtitles: English...

Syllabus - What you will learn from this course

Week
1
Hours to complete
2 hours to complete

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 videos (Total 31 min), 4 readings, 3 quizzes
Video5 videos
Motivations for linear algebra3m
Getting a handle on vectors9m
Operations with vectors11m
Summary1m
Reading4 readings
About Imperial College & the team5m
How to be successful in this course5m
Grading policy5m
Additional readings & helpful references10m
Quiz3 practice exercises
Solving some simultaneous equations15m
Exploring parameter space20m
Doing some vector operations12m
Week
2
Hours to complete
2 hours to complete

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 videos (Total 44 min), 4 quizzes
Video8 videos
Modulus & inner product9m
Cosine & dot product5m
Projection6m
Changing basis11m
Basis, vector space, and linear independence4m
Applications of changing basis3m
Summary1m
Quiz4 practice exercises
Dot product of vectors15m
Changing basis15m
Linear dependency of a set of vectors15m
Vector operations assessment15m
Week
3
Hours to complete
3 hours to complete

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 videos (Total 58 min), 3 quizzes
Video8 videos
How matrices transform space5m
Types of matrix transformation8m
Composition or combination of matrix transformations7m
Solving the apples and bananas problem: Gaussian elimination8m
Going from Gaussian elimination to finding the inverse matrix8m
Determinants and inverses12m
Summarym
Quiz2 practice exercises
Using matrices to make transformations12m
Solving linear equations using the inverse matrix16m
Week
4
Hours to complete
6 hours to complete

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 videos (Total 56 min), 4 quizzes
Video6 videos
Matrices changing basis11m
Doing a transformation in a changed basis6m
Orthogonal matrices8m
The Gram–Schmidt process6m
Example: Reflecting in a plane14m
Quiz2 practice exercises
Non-square matrix multiplication10m
Mappings to spaces with different numbers of dimensions12m
4.6
Career direction

20%

started a new career after completing these courses
Career Benefit

83%

got a tangible career benefit from this course

Top Reviews

By 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.

By 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.

Instructors

Avatar

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

About 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....

About the Mathematics for Machine Learning Specialization

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

Frequently Asked Questions

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

More questions? Visit the Learner Help Center.