Mathematics for Machine Learning: Linear Algebra
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.
More resources on Matrices
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Linear Algebra - Khan Academy
Learn linear algebra fundamentals, including matrices, vectors, and transformations, with Khan Academy's comprehensive course.
Eigenvectors and eigenvalues
Chapter 14 of 3Blue1Brown's Essence of Linear Algebra series. Grant Sanderson animates eigenvectors as the directions a transformation only stretches, then derives the characteristic equation and eigenbases, giving viewers geometric intuition behind the usual determinant-based computation and diagonalization.
3Blue1Brown Linear Algebra Series
Grant Sanderson's animated series on the geometric meaning of linear algebra: vectors, linear transformations, matrix multiplication, determinants, eigenvectors and abstract vector spaces. Viewers come away able to picture what a matrix does to space, which makes later computational courses far easier to follow.
Linear Algebra (MIT 18.06SC)
Matrix theory and linear algebra following Strang's textbook: elimination, vector spaces, orthogonality and least squares, determinants, eigenvalues, positive definite matrices and the singular value decomposition. Includes 74 lecture and problem-solving videos, summary notes, and problem sets and exams with solutions, built for independent study.
Essence of Linear Algebra
Grasp determinants with 3Blue1Brown's "Essence of Linear Algebra" course. Visualize and understand this key linear algebra concept.