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Last updated:

December 23, 2022


Unlimited Duration


This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration


This is a basic subject on matrix theory and linear algebra.

Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Course Curriculum

  • The geometry of linear equations Unlimited
  • Elimination with matrices Unlimited
  • Multiplication and inverse matrices Unlimited
  • Factorization into A = LU Unlimited
  • Transposes, permutations, spaces R^n Unlimited
  • Column space and nullspace Unlimited
  • Solving Ax = 0: pivot variables, special solutions Unlimited
  • Solving Ax = b: row reduced form R Unlimited
  • Independence, basis, and dimension Unlimited
  • The four fundamental subspaces Unlimited
  • Matrix spaces; rank 1; small world graphs Unlimited
  • Graphs, networks, incidence matrices Unlimited
  • Quiz 1 review Unlimited
  • Orthogonal vectors and subspaces Unlimited
  • Projections onto subspaces Unlimited
  • Projection matrices and least squares Unlimited
  • Orthogonal matrices and Gram-Schmidt Unlimited
  • Properties of determinants Unlimited
  • Determinant formulas and cofactors Unlimited
  • Cramer’s rule, inverse matrix, and volume Unlimited
  • Eigenvalues and eigenvectors Unlimited
  • Diagonalization and powers of A Unlimited
  • Differential equations and exp(At) Unlimited
  • Markov matrices; fourier series Unlimited
  • Quiz 2 review Unlimited
  • Symmetric matrices and positive definiteness Unlimited
  • Complex matrices; fast fourier transform Unlimited
  • Positive definite matrices and minima Unlimited
  • Similar matrices and Jordan form Unlimited
  • Singular value decomposition Unlimited
  • Linear transformations and their matrices Unlimited
  • Change of basis; image compression Unlimited
  • Quiz 3 review Unlimited
  • Left and right inverses; pseudoinverse Unlimited
  • Final course review Unlimited

About the instructor

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Massachusetts Institute of Technology