Home »Mathematics »MIT » Linear Algebra



Linear Algebra

Lecture 1: The Geometry of Linear Equations

Embed
Download:   mp3 download MP4,FLV & 3GP 58498 views

SEE: Guide to Download MIT Video Lecture

Course Description :

Contents:
The Geometry of Linear Equations - Elimination with Matrices-Multiplication and Inverse Matrices - Factorization into A = LU - Transposes, Permutations, Spaces R^n-Column Space and Nullspace -Solving Ax = 0: Pivot Variables, Special Solutions - Solving Ax = b: Row Reduced Form R - Independence, Basis, and Dimension - The Four Fundamental Subspaces - Matrix Spaces; Rank 1; Small World Graphs-Graphs, Networks, Incidence Matrices - Orthogonal Vectors and Subspaces - Projections onto Subspaces - Projection Matrices and Least Squares - Orthogonal Matrices and Gram - Schmidt

Properties of Determinants - Determinant Formulas and Cofactors - Cramers Rule, Inverse Matrix, and Volume - Eigenvalues and Eigenvectors - Diagonalization and Powers of A - Differential Equations and exp(At) - Markov Matrices - Fourier Series - Symmetric Matrices and Positive Definiteness - Complex Matrices - Fast Fourier Transform - Positive Definite Matrices and Minima - Similar Matrices and Jordan Form - Singular Value Decomposition - Linear Transformations and Their Matrices - Change of Basis - Image Compression - Left and Right Inverses - Pseudoinverse - Final Course Review

Other Resources :

Citation |

These free video lectures are licensed under a Creative Commons License by MIT OCW

Other Mathematics Courses

» check out the complete list of Mathematics lectures          

 

Get Your Degree!

Find schools and get information on the program that’s right for you.

Powered by Campus Explorer

Comments

Birajdar Gunvant Achutrao says :

All leacture on this web are very nice. Moreover they r helpful to others.

irfan says :

excellent approach

Post your Comments