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Mathematics for Machine Learning: Linear Algebra

Approx. 19 hours to complete

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Course Summary

This course covers the fundamentals of linear algebra and its applications in machine learning. You'll learn how to use linear algebra to solve problems in data analysis, image processing, and more.

Key Learning Points

Learn the basics of linear algebra and its applications to machine learning
Understand matrix operations and their applications in data analysis
Explore the use of linear algebra in image processing and computer vision

Job Positions & Salaries of people who have taken this course might have

- USA: $60,000 - $120,000
- India: ₹4,50,000 - ₹12,00,000
- Spain: €20,000 - €50,000
- USA: $60,000 - $120,000
- India: ₹4,50,000 - ₹12,00,000
- Spain: €20,000 - €50,000
- USA: $90,000 - $150,000
- India: ₹6,00,000 - ₹18,00,000
- Spain: €30,000 - €70,000
- USA: $60,000 - $120,000
- India: ₹4,50,000 - ₹12,00,000
- Spain: €20,000 - €50,000
- USA: $90,000 - $150,000
- India: ₹6,00,000 - ₹18,00,000
- Spain: €30,000 - €70,000
- USA: $100,000 - $160,000
- India: ₹7,00,000 - ₹20,00,000
- Spain: €35,000 - €80,000

Learning Outcomes

Understand the fundamentals of linear algebra
Apply linear algebra to solve problems in machine learning, data analysis, and image processing
Develop a strong foundation for further studies in machine learning and related fields

Prerequisites or good to have knowledge before taking this course

Basic understanding of calculus
Some programming experience in Python

Course Difficulty Level

Intermediate

Course Format

Online self-paced course
Video lectures
Hands-on exercises

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Applied Data Science with Python
Applied Machine Learning
Deep Learning

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Description

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.

Outline

Introduction to Linear Algebra and to Mathematics for Machine Learning
Introduction: Solving data science challenges with mathematics
Motivations for linear algebra
Getting a handle on vectors
Operations with vectors
Summary
About Imperial College & the team
How to be successful in this course
Grading policy
Additional readings & helpful references
Exploring parameter space
Solving some simultaneous equations
Doing some vector operations

Vectors are objects that move around space
Introduction to module 2 - Vectors
Modulus & inner product
Cosine & dot product
Projection
Changing basis
Basis, vector space, and linear independence
Applications of changing basis
Summary
Dot product of vectors
Changing basis
Linear dependency of a set of vectors
Vector operations assessment

Matrices in Linear Algebra: Objects that operate on Vectors
Matrices, vectors, and solving simultaneous equation problems
How matrices transform space
Types of matrix transformation
Composition or combination of matrix transformations
Solving the apples and bananas problem: Gaussian elimination
Going from Gaussian elimination to finding the inverse matrix
Determinants and inverses
Summary
Using matrices to make transformations
Solving linear equations using the inverse matrix

Matrices make linear mappings
Introduction: Einstein summation convention and the symmetry of the dot product
Matrices changing basis
Doing a transformation in a changed basis
Orthogonal matrices
The Gram–Schmidt process
Example: Reflecting in a plane
Non-square matrix multiplication
Example: Using non-square matrices to do a projection

Eigenvalues and Eigenvectors: Application to Data Problems
Welcome to module 5
What are eigenvalues and eigenvectors?
Special eigen-cases
Calculating eigenvectors
Changing to the eigenbasis
Eigenbasis example
Introduction to PageRank
Summary
Wrap up of this linear algebra course
Did you like the course? Let us know!
Selecting eigenvectors by inspection
Characteristic polynomials, eigenvalues and eigenvectors
Diagonalisation and applications
Eigenvalues and eigenvectors

Summary of User Reviews

Discover how linear algebra is used in machine learning with this comprehensive online course on Coursera. Students highly recommend this course for its clear explanations and practical examples.

Key Aspect Users Liked About This Course

Many users praised the practical examples used throughout the course, which helped to solidify their understanding of the material.

Pros from User Reviews

Clear and concise explanations
Practical examples that help to solidify understanding
Great course for beginners
Excellent instructor
Good pacing

Cons from User Reviews

Some users found the material too basic
Lack of interaction with instructor and other students
Lack of real-world applications
Limited scope of topics covered
Not enough exercises for practice

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