Imperial College – Mathematics for Machine Learning – Linear Algebra

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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.

Syllabus

1. Introduction to Linear Algebra and to Mathematics for Machine Learning
2. Vectors are objects that move around space
3. Matrices in Linear Algebra: Objects that operate on Vectors
4. Matrices make linear mappings
5. Eigenvalues and Eigenvectors: Application to Data Problems