mathworld.wolfram.com
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MathWorld is Wolfram's comprehensive online mathematics encyclopedia, featuring detailed, peer-reviewed articles on a wide range of topics. It includes entries on vector spaces and linear algebra with definitions, theorems, worked examples, formulas, diagrams, and references.
More resources on Vector Spaces
Linear Algebra Done Right - Sheldon Axler
Focuses on linear maps and operators, avoiding determinants until the end.
ocw.mit.edu
MIT OpenCourseWare provides free, openly accessible course materials from MIT across a wide range of subjects, including mathematics. It offers lecture notes, assignments, exams, and often video lectures, enabling self-study of topics like vector spaces.
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.
khanacademy.org
Khan Academy is a free online learning platform offering instructional videos and practice problems across math topics. Its Linear Algebra section covers vector spaces, bases, dimension, subspaces, and linear transformations, with guided tutorials and exercises.