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#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 21 hours to complete

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

#### English

Subtitles: English

### Skills you will gain

Eigenvalues And EigenvectorsBasis (Linear Algebra)Transformation MatrixLinear Algebra

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 21 hours to complete

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

#### English

Subtitles: English

### Syllabus - What you will learn from this course

Week
1
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....
5 videos (Total 28 min), 4 readings, 3 quizzes
5 videos
Motivations for linear algebra3m
Getting a handle on vectors9m
Operations with vectors11m
Summary1m
About Imperial College & the team5m
How to be successful in this course5m
3 practice exercises
Exploring parameter space20m
Solving some simultaneous equations15m
Doing some vector operations14m
Week
2
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....
8 videos (Total 44 min), 4 quizzes
8 videos
Modulus & inner product10m
Cosine & dot product5m
Projection6m
Changing basis11m
Basis, vector space, and linear independence4m
Applications of changing basis3m
Summary1m
4 practice exercises
Dot product of vectors15m
Changing basis15m
Linear dependency of a set of vectors15m
Vector operations assessment15m
Week
3
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....
8 videos (Total 57 min), 3 quizzes
8 videos
How matrices transform space5m
Types of matrix transformation8m
Composition or combination of matrix transformations8m
Solving the apples and bananas problem: Gaussian elimination8m
Going from Gaussian elimination to finding the inverse matrix8m
Determinants and inverses10m
Summary59s
2 practice exercises
Using matrices to make transformations12m
Solving linear equations using the inverse matrix16m
Week
4
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....
6 videos (Total 53 min), 4 quizzes
6 videos
Matrices changing basis11m
Doing a transformation in a changed basis4m
Orthogonal matrices6m
The Gram–Schmidt process6m
Example: Reflecting in a plane14m
2 practice exercises
Non-square matrix multiplication20m
Example: Using non-square matrices to do a projection12m
Week
5
4 hours to complete

## 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 videos (Total 44 min), 1 reading, 5 quizzes
9 videos
What are eigenvalues and eigenvectors?4m
Special eigen-cases3m
Calculating eigenvectors10m
Changing to the eigenbasis5m
Eigenbasis example7m
Introduction to PageRank8m
Summary1m
Wrap up of this linear algebra course1m
Did you like the course? Let us know!10m
4 practice exercises
Selecting eigenvectors by inspection20m
Characteristic polynomials, eigenvalues and eigenvectors30m
Diagonalisation and applications20m
Eigenvalues and eigenvectors25m
4.6
488 Reviews

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started a new career after completing these courses

## 31%

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### Top Reviews

By 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.

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

### David Dye

Professor of Metallurgy
Department of Materials

### Samuel J. Cooper

Lecturer
Dyson School of Design Engineering

### A. Freddie Page

Strategic Teaching Fellow
Dyson School of Design Engineering

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....