Paul's Online Notes - Orthogonality
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Detailed notes on orthogonal sets, bases, projections
More resources on Orthogonality
Gram-Schmidt Process
Clear walkthrough of Gram-Schmidt orthogonalization
Orthogonal complements | Chapter 11, Essence of linear algebra
3Blue1Brown explains orthogonal complements visually
Linear Algebra
Master orthogonality in linear algebra with this course from the Khan Academy Team! Explore vector spaces, projections, and more.
Linear Algebra
Learn orthogonality and linear algebra essentials with Gilbert Strang's renowned MIT course. Explore key concepts & problem-solving techniques!
ocw.mit.edu
MIT OpenCourseWare provides free, openly accessible course materials from MIT across dozens of disciplines, including mathematics. You can browse lecture notes, problem sets, exams, and video lectures to study topics like orthogonality at your own pace.
Mathematics for Machine Learning: Linear Algebra
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.