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MIT 18.06: Linear Algebra

Descriptions

  • Offered by: MIT (Professor Gilbert Strang)
  • Prerequisites: High school math
  • Difficulty: 🌟🌟🌟
  • Class Hour: 60+

MIT 18.06 is MIT's linear algebra course and the most popular linear algebra course in the world. Professor Gilbert Strang is a legend in the field, known for intuitive explanations emphasizing understanding over rote computation.

The course's core philosophy: linear algebra is not about matrix computation — it's about understanding linear spaces and linear transformations.

Course Resources

  • Website: ocw.mit.edu/18.06
  • Lectures: YouTube (MIT OCW, free)
  • Textbook: Introduction to Linear Algebra (Gilbert Strang, 5th Edition)

Course Content

Part 1: Vectors and Matrices

  • Vectors, matrices, linear systems
  • Elimination, matrix operations
  • Vector spaces, column space, null space

Part 2: Orthogonality and Projections

  • Dot product, orthogonality
  • Projections, least squares
  • Orthogonal bases, Gram-Schmidt

Part 3: Determinants and Eigenvalues

  • Determinant properties and computation
  • Eigenvalues and eigenvectors
  • Diagonalization

Part 4: Applications

  • Differential equations
  • Fourier series
  • Markov matrices
  • Linear programming

Self-Study Tips

Watch 3Blue1Brown's Essence of Linear Algebra first, then take this course. 3Blue1Brown builds intuition; Gilbert Strang builds the rigorous mathematical framework. Together, they're perfect.

Do the homework problems. Gilbert's problems are exceptionally well-designed.

Focus on Chapters 1-5 and 6-7. These topics (vector spaces, orthogonality, eigenvalues) are most used in AI and ML.

Notes

Gilbert Strang is over 80 years old, but his lectures remain clear and insightful. Many AI engineers say they gain new insights every time they revisit 18.06.

For advanced study, consider MIT 18.065 (Matrix Methods in Data Analysis, Signal Processing, and Machine Learning), designed specifically for AI-oriented students.