Matrix Methods in Data Analysis, Signal Processing, and Machine Learning (MIT 18.065)
by Gilbert Strang · MIT OpenCourseWare
Linear algebra for data science and deep learning: singular value decomposition, low-rank approximation, least squares, PCA, randomized linear algebra, gradient descent and the structure of neural networks. Includes 37 lecture videos and problem sets. Afterwards you can recognise the matrix computations inside modern machine learning.
More resources on Applications of Linear Algebra
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.
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.
Mathematics for Machine Learning
A free textbook by Deisenroth, Faisal and Ong (Cambridge University Press) covering the linear algebra, analytic geometry, matrix decompositions, vector calculus and probability behind machine learning, then derives linear regression, PCA, Gaussian mixtures and support vector machines from them.
Vectors | Chapter 1, Essence of Linear Algebra
Opening chapter of Grant Sanderson's animated linear algebra series, contrasting the physics, computer science and mathematics views of vectors. Shows vectors as arrows and coordinate lists, and how addition and scalar multiplication work geometrically, laying intuition for linear combinations and transformations.
Computational Science and Engineering I (MIT 18.085)
Applied linear algebra for networks, structures and estimation, followed by equilibrium differential equations, Laplace's equation, boundary-value problems, calculus of variations, Fourier series and the discrete Fourier transform. Includes 50 lecture videos, problem sets and exams with solutions, and programming assignments.
Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares (free PDF)
Stanford and UCLA authors' applied linear algebra text, free PDF from Cambridge. Covers solving square and overdetermined systems via QR factorization and back substitution, with operation counts, so you understand what a solver actually does and when least squares replaces exact solution.