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Linear Algebra (MIT)

Created/Published/Taught by:
Massachusetts Institute of Technology
Gilbert Strang

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“This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering….

This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course.”

The course covers the following topics:

  • Systems of linear equations
  • Row reduction and echelon forms
  • Matrix operations, including inverses
  • Block matrices
  • Linear dependence and independence
  • Subspaces and bases and dimensions
  • Orthogonal bases and orthogonal projections
  • Gram-Schmidt process
  • Linear models and least-squares problems
  • Determinants and their properties
  • Cramer’s Rule
  • Eigenvalues and eigenvectors
  • Diagonalization of a matrix
  • Symmetric matrices
  • Positive definite matrices
  • Similar matrices
  • Linear transformations
  • Singular Value Decomposition

Recommended Prerequisites: Multivariable Calculus "is a formal prerequisite for MIT students wishing to enroll…but knowledge of calculus is not required to learn the subject. To succeed in this course you will need to be comfortable with vectors, matrices, and three-dimensional coordinate systems."

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