MIT / Science / Mathematics
Lecture : The geometry of linear equations
By Gilbert Strang | Linear Algebra
Lecture 1 of 35
Rate this lecture -      More Lectures - Select Lecture...1 : The geometry of linear equations2 : Elimination with matrices3 : Multiplication and inverse matrices4 : Factorization into A LU5 : Transposes permutations, spaces R n6 : Column space and nullspace7 : Solving Ax = 0 pivot variables special solutions8 : Solving Ax = b row reduced form R9 : Independence basis and dimension10 : The four fundamental subspaces11 : Matrix spaces rank 1 small world graphs12 : Graphs networks incidence matrices13 : Quiz 1 review14 : Orthogonal vectors and subspaces15 : Projections onto subspaces16 : Projection matrices and least squares17 : Orthogonal matrices and Gram Schmidt18 : Properties of determinants19 : Determinant formulas and cofactors20 : Cramers rule inverse matrix and volume21 : Eigenvalues and eigenvectors22 : Diagonalization and powers of A23 : Differential equations and exp(At)24 : Markov matrices fourier series25 : Quiz 2 review26 : Symmetric matrices and positive definiteness27 : Complex matrices fast fourier transform28 : Positive definite matrices and minima29 : Similar matrices and jordan form30 : Singular value decomposition31 : Linear transformations and their matrices32 : Change of basis image compression33 : Quiz 3 review34 : Left and right inverses pseudoinverse35 : Final course review

Course Description
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.
Courses Index
1 : Introductory Probability and Statistics for Business   (Fletcher Ibser / Berkeley)
2 : Analytic Geometry and Calculus   (Thomas Scanlon / Berkeley)
3 : Introduction to Probability and Statistics   (Deborah NOLAN / Berkeley)
4 : Single Variable Calculus   (David Jerison / MIT)
5 : Multivariable Calculus   (Denis Auroux / MIT)
6 : Differential Equations   (Haynes Miller / MIT)
7 : Computational Science and Engineering I   (Gilbert Strang / MIT)
8 : Mathematical Methods for Engineers II   (Gilbert Strang / MIT)
9 : Multivariable Calculus   (Michael HUTCHINGS / Berkeley)
10 : Calculus I   (Richard Delaware / University of Missouri)
11 : College Algebra   (Richard Delaware / University of Missouri)
12 : Homework Help for Multivariable Calculus   (Multiple Instructors / MIT)
13 : Homework Help for Single Variable Calculus   (Multiple Instructors / MIT)
14 : Probability for Math Science   (Herbert Enderton / UCLA)
15 : Differential and Integral Calculus   (Steve Butler / UCLA)