A complete lecture series for Stanford University's ENGR108: Introduction to Applied Linear Algebra (Vectors, Matrices, and Least Squares) taught by Professor Stephen Boyd.

Course Overview

ENGR108 covers the grammar and practical mechanics of applied linear algebra, emphasizing engineering and data science applications over abstract theorem-proving. The curriculum introduces vectors, matrices, and least squares methods with practical implementations in Julia and Python.

Core Topics Covered

  1. Vectors and Vector Spaces: Vector addition, scalar multiplication, inner products, norms, angles, Cauchy-Schwarz inequality, distances, and standard orthonormal bases.
  2. Linear Functions & Models: Affine functions, Taylor series approximations, linear models, regression setups, and geometric projections.
  3. Matrices and Transformations: Matrix multiplication, inverses, transposes, block matrices, matrix-vector products, and linear equations.
  4. Least Squares Approximations: Overdetermined systems, least squares fitting, objective formulations, normal equations, and regularized least squares (ridge regression).
  5. Constrained Optimization & Applications: Constrained least squares, Lagrange multipliers, data fitting, tomographic reconstruction, and control applications.

About Professor Stephen Boyd

Stephen P. Boyd is the Samsung Professor in the School of Engineering and Professor of Electrical Engineering at Stanford University. He is an internationally recognized authority on convex optimization, linear algebra, control system engineering, and signal processing.