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This is a basic subject on matrix theory and linear algebra.
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1
English
English [CC]
FREE
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Description
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 content
- 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
Instructor
Massachusetts Institute of Technology
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1916
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