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Linear Algebra (MIT)
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Course Level: Freshman
Course Level: Freshman
Course Description:
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.
Prerequisites
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 1 - The Geometry of Linear Equations.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 2 - Elimination with Matrices.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 3 - Multiplication and Inverse Matrices.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 4 - Factorization into A = LU.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 5 - Transposes, Permutations, Spaces R^n.jpg){kind=spacer}
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 6 - Column Space and Nullspace.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 7 - Solving Ax = 0; Pivot Variables, Special Solutions.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 8 - Solving Ax = b; Row Reduced Form R.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 9 - Independence, Basis, and Dimension.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 10 - The Four Fundamental Subspaces.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 11 - Matrix Spaces; Rank 1; Small World Graphs.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 12 - Graphs, Networks, Incidence Matrices.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 13 - Quiz 1 Review.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 14 - Orthogonal Vectors and Subspaces.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 15 - Projections onto Subspaces.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 16 - Projection Matrices and Least Squares.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 17 - Orthogonal Matrices and Gram-Schmidt.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 18 - Properties of Determinants.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 19 - Determinant Formulas and Cofactors.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 20 - Cramer's Rule, Inverse Matrix, and Volume.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 21 - Eigenvalues and Eigenvectors.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 22 - Diagonalization and Powers of A.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 23 - Differential Equations and exp(At).jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 24 - Markov Matrices; Fourier Series.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 25 - Quiz 2 Review.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 26 - Symmetric Matrices and Positive Definiteness.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 27 - Complex Matrices; Fast Fourier Transform.jpg){kind=spacer}
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 28 - Positive Definite Matrices and Minima.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 29 - Similar Matrices and Jordan Form.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 30 - Singular Value Decomposition.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 31 - Linear Transformations and Their Matrices.jpg){kind=spacer}
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 32 - Change of Basis; Image Compression.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 33 - Quiz 3 Review.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 34 - Left and Right Inverses; Pseudoinverse.jpg)
 - MIT - Gilbert Strang - BYNCSA/Thumbnails/Lecture 35 - Final Course Review.jpg)
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