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 10: The Four Fundamental Subspaces (18.06)
The lecture introduces the crucial concepts of the column space, null space, row space, and left null space of a matrix, elucidating their interrelationships and orthogonal properties.
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
Lecture 9: Independence, Basis, and Dimension (18.06)
Next · Lecture 11Lecture 11: Matrix Spaces; Rank 1; Small World Graphs (18.06)