Linear Algebra

This is a basic course 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.

Lectures

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   Lecture 1 - The Geometry of Linear Equations

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   Lecture 2 - Elimination with Matrices

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   Lecture 3 - Multiplication and Inverse Matrices

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   Lecture 4 - Factorization into A = LU

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   Lecture 5 - Transposes, Permutations, Spaces R^n

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   Lecture 6 - Column Space and Nullspace

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   Lecture 7 - Solving Ax = 0: Pivot Variables, Special Solutions

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   Lecture 8 - Solving Ax = b: Row Reduced Form R

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   Lecture 9 - Independence, Basis, and Dimension

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    Lecture 10 - The Four Fundamental Subspaces

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    Lecture 11 - Matrix Spaces; Rank 1; Small World Graphs

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    Lecture 12 - Graphs, Networks, Incidence Matrices

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    Lecture 13 - Quiz 1 Review

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    Lecture 14 - Orthogonal Vectors and Subspaces

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    Lecture 15 - Projections onto Subspaces

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    Lecture 16 - Projection Matrices and Least Squares

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    Lecture 17 - Orthogonal Matrices and Gram-Schmidt

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    Lecture 18 - Properties of Determinants

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    Lecture 19 - Determinant Formulas and Cofactors

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    Lecture 20 - Cramer's Rule, Inverse Matrix, and Volume

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    Lecture 21 - Eigenvalues and Eigenvectors

    In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

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    Lecture 22 - Diagonalization and Powers of A

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    Lecture 23 - Differential Equations and exp(At)

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    Lecture 24 - Markov Matrices; Fourier Series

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    Lecture 25 - Quiz 2 Review

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    Lecture 26 - Symmetric Matrices and Positive Definiteness

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    Lecture 27 - Complex Matrices; Fast Fourier Transform

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    Lecture 28 - Positive Definite Matrices and Minima

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    Lecture 29 - Similar Matrices and Jordan Form

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    Lecture 30 - Singular Value Decomposition

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    Lecture 31 - Linear Transformations and Their Matrices

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    Lecture 32 - Change of Basis; Image Compression

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    Lecture 33 - Quiz 3 Review

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    Lecture 34 - Left and Right Inverses; Pseudoinverse

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    Lecture 35 - Final Course Review