# Linear Algebra

Massachusetts Institute of Technology

This is a basic course 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.

• ##### The Geometry of Linear Equations
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Elimination with Matrices
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Multiplication and Inverse Matrices
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Factorization into A = LU
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Transposes, Permutations, Spaces R^n
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Column Space and Nullspace
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Solving Ax = 0: Pivot Variables, Special Solutions
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Solving Ax = b: Row Reduced Form R
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Independence, Basis, and Dimension
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### The Four Fundamental Subspaces
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Matrix Spaces; Rank 1; Small World Graphs
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Graphs, Networks, Incidence Matrices
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Quiz 1 Review
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Orthogonal Vectors and Subspaces
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Projections onto Subspaces
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Projection Matrices and Least Squares
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Orthogonal Matrices and Gram-Schmidt
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Properties of Determinants
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Determinant Formulas and Cofactors
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Cramer's Rule, Inverse Matrix, and Volume
Gilbert Strang

Catherine Brown gives the first lecture in the D.H. Lawrence series

• ##### Eigenvalues and Eigenvectors
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• ##### Diagonalization and Powers of A
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• ##### Differential Equations and exp(At)
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• ##### Markov Matrices; Fourier Series
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• ##### Quiz 2 Review
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• ##### Symmetric Matrices and Positive Definiteness
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• ##### Complex Matrices; Fast Fourier Transform
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• ##### Positive Definite Matrices and Minima
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• ##### Similar Matrices and Jordan Form
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• ##### Singular Value Decomposition
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• ##### Linear Transformations and Their Matrices
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• ##### Change of Basis; Image Compression
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• ##### Quiz 3 Review
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• ##### Left and Right Inverses; Pseudoinverse
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.

• ##### Final Course Review
Gilbert Strang

In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.