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Linear Algebra

Linear algebra studies spaces and transformations that preserve addition and scaling. A durable learning sequence is:

  1. vectors, span, independence, basis, and dimension;
  2. linear maps and their matrix representations;
  3. systems of equations, elimination, rank, and null spaces;
  4. inner products, orthogonality, projections, and least squares;
  5. determinants, eigenvalues, and eigenvectors;
  6. singular value decomposition and low-rank approximation;
  7. applications to optimization, data analysis, and machine learning.

This is currently a seed map. MIT OpenCourseWare 18.06SC supplies a complete course path; the site should grow focused notes only where derivations or applications become repeatedly useful.