Jupyter Notebooks

Course notebooks provide executable demonstrations and exercises for numerical matrix computation, exact symbolic computation, visualization, and experimentation.

Demonstrations

Instructor demonstrations illustrate linear algebra concepts and connect algebraic calculations with geometric interpretation.

  • Matrix Computation: NumPy and SymPy โ€” a companion to Lecture 00 introducing numerical and exact matrix calculations, linear systems, least squares, and responsible computation
  • Systems and Matrices โ€” the reviewed companion to Lecture 01, combining exact SymPy elimination, back substitution, and classification with NumPy solves, residual checks, and the resistance-network exercise
  • Inverses and Invertibility โ€” a draft companion to Lecture 02 combining pivot tests, exact inverses, singular systems, direct solves, and the Leontief and precision applications
  • Matrix Structure and Transformations โ€” a draft companion to Lecture 03 exploring matrix patterns, SciPy PLU factorization, basis images, geometric transformations, and composition
  • Determinants โ€” a locally validated draft companion to Lecture 04 exploring signed area, row operations, PLU determinants, eigenvalue products, and numerical scaling
  • Euclidean Vector Spaces โ€” a locally validated draft companion to Lecture 05 exploring point coordinates, homogeneous directions, affine solution sets, projection onto a line, and three-dimensional displacement geometry
  • Vector Spaces, Subspaces, and Span โ€” a locally validated draft companion exploring polynomial and function vectors, symbolic closure tests, span membership, and affine sets
  • Bases, Dimension, and Coordinates โ€” a locally validated draft companion exploring basis extraction, redundant generators, matrix and polynomial coordinates, and change of basis
  • Matrix Spaces and Rank โ€” a locally validated draft companion exploring the four fundamental spaces, rank factorization, compatibility, all solutions, and matrices of linear maps

Exercises

Student exercises will provide opportunities to explore matrices, vector spaces, transformations, eigenvalues, and inner products computationally. Exercise notebooks will be linked here after they have been developed and validated.