Mathematics for Machine Learning: Linear Algebra from Coursera

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.

What's inside

Syllabus

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.

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.

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.

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.

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.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Teaches mathematical intuition, which helps learners understand linear algebra problems

Develops vectors and matrices, which are core skills for data-driven applications

Hands-on labs help learners apply the concepts discussed in the course

Emphasizes the practical aspects of linear algebra, which is beneficial for students interested in data science and machine learning

Provides foundational skills and knowledge in linear algebra, which is useful for further studies in machine learning

Reviews summary

Mathematics for machine learning: linear algebra

learners say 'Mathematics for Machine Learning: Linear Algebra' is a thoughtfully-designed course that provides a strong foundation in the topic's fundamentals. They appreciate the diverse range of materials (lectures, readings, assignments), many of which include real-world applications that help make the concepts more relatable and engaging. The course is described as challenging, but not overly so; instructors provide clear explanations and make themselves available for questions.

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Mathematics for Machine Learning: Linear Algebra with these activities:

Introduction to Linear Algebra by Gilbert Strang

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Review a classic textbook on linear algebra to strengthen your foundation. Engage with clear explanations, insightful examples, and thought-provoking exercises to enhance your understanding of core concepts.

View Introduction to Linear Algebra (Gilbert Strang) on Amazon

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Read through the assigned chapters
Solve the practice problems
Summarize key concepts

Peer Study and Problem-Solving Sessions

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Form study groups with peers to reinforce concepts, work through exercises, and prepare for assessments. Collaborative learning can enhance your understanding and build a supportive learning community.

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Find a study partner or group
Schedule regular study sessions
Create a study plan
Work through problems and exercises together
Discuss concepts and share insights

Solving Linear Equations and Matrix Problems

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Solve linear equation systems and practice matrix operations to enhance your algebraic skills and solidify your understanding of fundamental concepts in linear algebra.

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Review Gaussian elimination
Work through practice problems involving matrix multiplication
Find determinants and solve matrix equations
Apply these techniques to solve real-world problems

Five other activities

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Vector and Matrix Operations for Image Processing

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Develop your understanding of how vector and matrix operations are used in image processing. Implement these operations and apply them to real-world image manipulation tasks.

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Review vector and matrix basics
Learn about image representation using vectors and matrices
Implement image transformations, such as rotations and scaling
Use linear algebra techniques to analyze image data

Kaggle Linear Algebra Competition

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Challenge yourself in aKaggle competition focused on linear algebra. Apply your skills to solve real-world problems, compete with others, and enhance your practical knowledge.

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Identify relevant Kaggle competitions
Study the competition guidelines
Develop a solution using linear algebra techniques
Submit your solution and track your progress (optional)

Matrix Decomposition Techniques

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Explore different matrix decomposition techniques and their applications in machine learning algorithms. Gain hands-on experience in implementing these techniques and interpreting the results.

Browse courses on Singular Value Decomposition

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Learn about the concepts of eigenvalues and eigenvectors
Follow tutorials on singular value decomposition and its applications
Implement matrix factorization techniques in a coding environment
Analyze and interpret the results of matrix decomposition

Data Visualization with Linear Algebra

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Utilize linear algebra concepts to visualize and explore data effectively. Create interactive visualizations that showcase your understanding of dimensionality reduction and data transformation techniques.

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Research different data visualization libraries
Learn about PCA (Principal Component Analysis)
Implement PCA in a coding environment
Create visualizations using linear algebra techniques
Present your findings and insights

Linear Algebra Portfolio Project

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Showcase your proficiency in linear algebra by completing a portfolio project. Select a real-world problem that can be solved using linear algebra techniques and develop a comprehensive solution.

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Brainstorm project ideas
Research and select a suitable project
Develop a project plan
Implement your solution
Write a project report

Career center

Learners who complete Mathematics for Machine Learning: Linear Algebra will develop knowledge and skills that may be useful to these careers:

Data Scientist

Data Scientists are responsible for using data to solve complex problems and gain new insights. This course can help Data Scientists build a strong foundation in linear algebra, which is a fundamental tool for working with data. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating data. Additionally, the course provides hands-on experience with Python, which is a popular programming language for data science.

See salaries and explore the career path for Data Scientist

Machine Learning Engineer

Machine Learning Engineers design and build machine learning models to solve real-world problems. This course can help Machine Learning Engineers build a strong foundation in linear algebra, which is a fundamental tool for working with machine learning models. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating machine learning models. Additionally, the course provides hands-on experience with Python, which is a popular programming language for machine learning.

See salaries and explore the career path for Machine Learning Engineer

Quantitative Analyst

Quantitative Analysts use mathematical and statistical techniques to analyze data and make predictions. This course can help Quantitative Analysts build a strong foundation in linear algebra, which is a fundamental tool for working with data. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating data. Additionally, the course provides hands-on experience with Python, which is a popular programming language for quantitative analysis.

See salaries and explore the career path for Quantitative Analyst

Operations Research Analyst

Operations Research Analysts use mathematical and statistical techniques to solve complex problems in business and industry. This course can help Operations Research Analysts build a strong foundation in linear algebra, which is a fundamental tool for working with data. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating data. Additionally, the course provides hands-on experience with Python, which is a popular programming language for operations research.

See salaries and explore the career path for Operations Research Analyst

Statistician

Statisticians collect, analyze, and interpret data to help businesses and organizations make informed decisions. This course can help Statisticians build a strong foundation in linear algebra, which is a fundamental tool for working with data. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating data. Additionally, the course provides hands-on experience with Python, which is a popular programming language for statistics.

See salaries and explore the career path for Statistician

Actuary

Actuaries use mathematical and statistical techniques to assess risk and make financial decisions. This course can help Actuaries build a strong foundation in linear algebra, which is a fundamental tool for working with data. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating data. Additionally, the course provides hands-on experience with Python, which is a popular programming language for actuarial science.

See salaries and explore the career path for Actuary

Financial Analyst

Financial Analysts use mathematical and statistical techniques to analyze financial data and make investment recommendations. This course can help Financial Analysts build a strong foundation in linear algebra, which is a fundamental tool for working with data. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating data. Additionally, the course provides hands-on experience with Python, which is a popular programming language for financial analysis.

See salaries and explore the career path for Financial Analyst

Market Researcher

Market Researchers collect and analyze data to understand consumer behavior and trends. This course can help Market Researchers build a strong foundation in linear algebra, which is a fundamental tool for working with data. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating data. Additionally, the course provides hands-on experience with Python, which is a popular programming language for market research.

See salaries and explore the career path for Market Researcher

Business Analyst

Business Analysts use data to help businesses make informed decisions. This course can help Business Analysts build a strong foundation in linear algebra, which is a fundamental tool for working with data. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating data. Additionally, the course provides hands-on experience with Python, which is a popular programming language for business analysis.

See salaries and explore the career path for Business Analyst

Data Analyst

Data Analysts collect, analyze, and interpret data to help businesses make informed decisions. This course can help Data Analysts build a strong foundation in linear algebra, which is a fundamental tool for working with data. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating data. Additionally, the course provides hands-on experience with Python, which is a popular programming language for data analysis.

See salaries and explore the career path for Data Analyst

Software Engineer

Software Engineers design, develop, and maintain software applications. This course can help Software Engineers build a strong foundation in linear algebra, which is a fundamental tool for working with data. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating data. Additionally, the course provides hands-on experience with Python, which is a popular programming language for software development.

See salaries and explore the career path for Software Engineer

Computer Scientist

Computer Scientists design and develop computer systems and software applications. This course can help Computer Scientists build a strong foundation in linear algebra, which is a fundamental tool for working with data. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating data. Additionally, the course provides hands-on experience with Python, which is a popular programming language for computer science.

See salaries and explore the career path for Computer Scientist

Mathematician

Mathematicians study the patterns and structures of numbers, shapes, and other mathematical objects. This course can help Mathematicians build a strong foundation in linear algebra, which is a fundamental tool for working with data. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating data. Additionally, the course provides hands-on experience with Python, which is a popular programming language for mathematics.

See salaries and explore the career path for Mathematician

Physicist

Physicists study the laws of nature and the behavior of matter and energy. This course can help Physicists build a strong foundation in linear algebra, which is a fundamental tool for working with data. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating data. Additionally, the course provides hands-on experience with Python, which is a popular programming language for physics.

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Engineer

Engineers design, develop, and maintain machines, structures, and other systems. This course can help Engineers build a strong foundation in linear algebra, which is a fundamental tool for working with data. The course covers topics such as vectors, matrices, eigenvalues, and eigenvectors, which are all essential for understanding and manipulating data. Additionally, the course provides hands-on experience with Python, which is a popular programming language for engineering.

See salaries and explore the career path for Engineer