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MIT 18.06: Linear Algebra →0/20
1

The Geometry of Linear Equations

39:49
2

Elimination with Matrices

47:42
3

Matrix Multiplication and Inverse Matrices

46:30
4

Factorization into A = LU

48:05
5

Transposes, Permutations & Vector Spaces R^n

47:41
6

Column Space and Nullspace

46:01
7

Solving Ax = 0 — Pivot Variables, Free Variables & Rank

43:19
8

Solving Ax = b — Complete Solutions & Full Rank Cases

47:19
9

Independence, Basis, and Dimension

50:14
10

The Four Fundamental Subspaces

49:20
11

Matrix Spaces; Rank 1; Small World Graphs

45:56
12

Graphs, Networks, Incidence Matrices

47:57
13

Orthogonal Vectors and Subspaces

49:48
14

Projections onto Subspaces

48:51
15

Projection Matrices and Least Squares

48:05
16

Orthogonal Matrices and Gram-Schmidt

49:10
17

Properties of Determinants

49:12
18

Determinant Formulas and Cofactors

53:17
19

Cramer's Rule, Inverse Matrix, and Volume

51:01
20

Eigenvalues and Eigenvectors

51:23

Matrix Spaces; Rank 1; Small World Graphs

Gilbert StrangDistinguishedMIT

Professor

45:56·2009·undergraduate level

This lecture examines different types of matrix spaces, with a focus on rank-1 matrices and their construction. It also introduces the concept of small-world graphs as an application.

MathematicsLinear AlgebraMatrix SpacesRank-1 MatricesGraph Theory

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

LecturerAll lecturers →
Gilbert StrangDistinguished

MIT Professor Emeritus & Author of Introduction to Linear Algebra

MIT Professor of Mathematics Emeritus whose legendary 18.06 Linear Algebra and 18.085 Computational Science courses educated millions of engineers and mathematicians.

3 courses · 56 lecturesCanon
Previous · Lecture 10

The Four Fundamental Subspaces

Next · Lecture 12

Graphs, Networks, Incidence Matrices

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