2017-06-02

Linear Algebra (Spring 2005) by Gilbert Strang at MIT

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source: MIT OpenCourseWare     2009年5月6日
MIT 18.06 Linear Algebra, Spring 2005
Instructor: Prof. Gilbert Strang
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. *Please note that lecture 4 is unavailable in a higher quality format.
Find more lecture notes, study materials, and more courses at http://ocw.mit.edu.
View the complete course at: http://ocw.mit.edu/18-06S05

Lec 1 39:49 The Geometry of Linear Equations.
Lec 2 47:42 Elimination with Matrices.
Lec 3 46:49 Multiplication and Inverse Matrices.
Lec 4 Factorization into A = LU 48:05
Lec 5 47:42 Transposes, Permutations, Spaces R^n.
Lec 6 46:01 Column Space and Nullspace.
Lec 7 43:20 Solving Ax = 0: Pivot Variables, Special Solutions.
Lec 8 47:20 Solving Ax = b: Row Reduced Form R.
Lec 9 50:14 Independence, Basis, and Dimension.
Lec 10 49:20 The Four Fundamental Subspaces.
Lec 11 45:56 Matrix Spaces; Rank 1; Small World Graphs.
Lec 12 47:57 Graphs, Networks, Incidence Matrices.
Lec 13 47:40 Quiz 1 Review.
Lec 14 49:48 Orthogonal Vectors and Subspaces.
Lec 15 48:51 Projections onto Subspaces.
Lec 16 48:05 Projection Matrices and Least Squares
Lec 17 49:25 Orthogonal Matrices and Gram-Schmidt.
Lec 18 49:12 Properties of Determinants.
Lec 19 53:17 Determinant Formulas and Cofactors.
Lec 20 51:01 Cramer's Rule, Inverse Matrix, and Volume.
Lec 21 51:23 Eigenvalues and Eigenvectors.
Lec 22 51:51 Diagonalization and Powers of A.
Lec 23 51:03 Differential Equations and exp(At).
Lec 24 51:12 Markov Matrices; Fourier Series.*
Lec 24b 48:20 Quiz 2 Review. * NOTE: the audio is in the right channel only. If you hear no audio, you are listening only to the left channel.
Lec 25 43:52 Symmetric Matrices and Positive Definiteness. * NOTE: the audio is in the right channel only. If you hear no audio, you are listening only to the left channel.
Lec 26 47:52 Complex Matrices; Fast Fourier Transform.
Lec 27 50:40 Positive Definite Matrices and Minima.
Lec 28 45:56 Similar Matrices and Jordan Form.
Lec 29 41:35 Singular Value Decomposition.
Lec 30 49:27 Linear Transformations and Their Matrices.
Lec 31 50:14 Change of Basis; Image Compression.
Lec 32 47:06 Quiz 3 Review.
Lec 33 41:53 Left and Right Inverses; Pseudoinverse.
Lec 34 43:26 Final Course Review.