Lecture 1: The Geometry of Linear Equations (18.06)
39:49Elimination with Matrices
47:42Matrix Multiplication and Inverse Matrices
46:30MIT 18.06 Lecture 4: Factorization into A = LU
48:05MIT 18.06 Lecture 5: Transposes, Permutations & Vector Spaces R^n
47:41MIT 18.06 Lecture 6: Column Space and Nullspace
46:01MIT 18.06 Lecture 7: Solving Ax = 0 — Pivot Variables, Free Variables & Rank
43:19MIT 18.06 Lecture 8: Solving Ax = b — Complete Solutions & Full Rank Cases
47:19Lecture 9: Independence, Basis, and Dimension (18.06)
50:14Lecture 10: The Four Fundamental Subspaces (18.06)
49:20Lecture 11: Matrix Spaces; Rank 1; Small World Graphs (18.06)
45:56Lecture 12: Graphs, Networks, Incidence Matrices (18.06)
47:57Lecture 14: Orthogonal Vectors and Subspaces (18.06)
49:48Lecture 15: Projections onto Subspaces (18.06)
48:51Lecture 16: Projection Matrices and Least Squares (18.06)
48:05Lecture 17: Orthogonal Matrices and Gram-Schmidt (18.06)
49:10Lecture 18: Properties of Determinants (18.06)
49:12Lecture 19: Determinant Formulas and Cofactors (18.06)
53:17Lecture 20: Cramer's Rule, Inverse Matrix, and Volume (18.06)
51:01Lecture 21: Eigenvalues and Eigenvectors (18.06)
51:23The Geometry of Linear Equations
39:49Lecture 9: Independence, Basis, and Dimension (18.06)
This session rigorously defines linear independence, spanning sets, and basis vectors, culminating in the formal definition of dimension for vector spaces and subspaces.
MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
MIT 18.06 Lecture 8: Solving Ax = b — Complete Solutions & Full Rank Cases
Next · Lecture 10Lecture 10: The Four Fundamental Subspaces (18.06)