The Geometry of Linear Equations
39:49Elimination with Matrices
47:42Matrix Multiplication and Inverse Matrices
46:30Factorization into A = LU
48:05Transposes, Permutations & Vector Spaces R^n
47:41Column Space and Nullspace
46:01Solving Ax = 0 — Pivot Variables, Free Variables & Rank
43:19Solving Ax = b — Complete Solutions & Full Rank Cases
47:19Independence, Basis, and Dimension
50:14The Four Fundamental Subspaces
49:20Matrix Spaces; Rank 1; Small World Graphs
45:56Graphs, Networks, Incidence Matrices
47:57Orthogonal Vectors and Subspaces
49:48Projections onto Subspaces
48:51Projection Matrices and Least Squares
48:05Orthogonal Matrices and Gram-Schmidt
49:10Properties of Determinants
49:12Determinant Formulas and Cofactors
53:17Cramer's Rule, Inverse Matrix, and Volume
51:01Eigenvalues and Eigenvectors
51:23Orthogonal Matrices and Gram-Schmidt
This session introduces orthogonal matrices and their properties, followed by a detailed explanation of the Gram-Schmidt orthonormalization process for constructing orthonormal bases.
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
Projection Matrices and Least Squares
Next · Lecture 17Properties of Determinants