**Course Description**

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.

**Lecture Videos**

Lecture 1: The geometry of linear equations (Watch Here)

Lecture 2: Elimination with matrices (Watch Here)

Lecture 3: Multiplication and inverse matrices (Watch Here)

Lecture 4: Factorization into A = LU (Watch Here)

Lecture 5: Transposes, permutations, spaces R^n (Watch Here)

Lecture 6: Column space and nullspace (Watch Here)

Lecture 7: Solving Ax = 0: pivot variables, special solutions (Watch Here)

Lecture 8: Solving Ax = b: row reduced form R (Watch Here)

Lecture 9: Independence, basis, and dimension (Watch Here)

Lecture 10: The four fundamental subspaces (Watch Here)

Lecture 11: Matrix spaces; rank 1; small world graphs (Watch Here)

Lecture 12: Graphs, networks, incidence matrices (Watch Here)

Lecture 13: Quiz 1 review (Watch Here)

Lecture 14: Orthogonal vectors and subspaces (Watch Here)

Lecture 15: Projections onto subspaces (Watch Here)

Lecture 16: Projection matrices and least squares (Watch Here)

Lecture 17: Orthogonal matrices and Gram-Schmidt (Watch Here)

Lecture 18: Properties of determinants (Watch Here)

Lecture 19: Determinant formulas and cofactors (Watch Here)

Lecture 20: Cramer's rule, inverse matrix, and volume (Watch Here)

Lecture 21: Eigenvalues and eigenvectors (Watch Here)

Lecture 22: Diagonalization and powers of A (Watch Here)

Lecture 23: Differential equations and exp(At) (Watch Here)

Lecture 24: Markov matrices; fourier series (Watch Here)

Lecture 24b: Quiz 2 review (Watch Here)

Lecture 25: Symmetric matrices and positive definiteness (Watch Here)

Lecture 26: Complex matrices; fast fourier transform (Watch Here)

Lecture 27: Positive definite matrices and minima (Watch Here)

Lecture 28: Similar matrices and jordan form (Watch Here)

Lecture 29: Singular value decomposition (Watch Here)

Lecture 30: Linear transformations and their matrices (Watch Here)

Lecture 31: Change of basis; image compression (Watch Here)

Lecture 32: Quiz 3 review (Watch Here)

Lecture 33: Left and right inverses; pseudoinverse (Watch Here)

Lecture 34: Final course review (Watch Here)

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