Within the field of mathematics I handle every day linear algebra plays a vital role. Linear algebra is a field of mathematics that studies vectors and vector spaces. On common use of linear algebra is to solve a set of linear equations. Personally I learned it in university using a book by David C. Lay called Linear Algebra and Its Applications. It is a perfectly good book, and I can recommend it if you want to have a book on the topic.
The reason why I bring up the topic, is that I rediscovered a video version a MIT course in linear algebra taught by Gilbert Strang. I found the videos when I first studied to my exam in linear algebra. I think he teaches it in a very understandable manner. All of the videos can be found at Academic Earth. However, I think that the videos there are poor quality, so I have compiled a list of the videos representing the course in a better quality.
In order to understand Linear algebra you will need a basic understanding of vectors and matrices. Not much, but you need to know what a vector is. After seeing the course titles I can see that I should probably review a few of the topics again.
The course is not that fast paced but he is thorough and a good teacher. Each episode is a little under an hour, so prepare to use a weeks worth of work just watching the lectures.
The last thing I will push to you is the linear algebra book by Gilbert Strang, which is also the course material for the video course. It is called Introduction to Linear Algebra. I have embedded the first video for your pleasure, and all the videos are linked below.
Lecture 1 – The Geometry of Linear Equations
Lecture 2 – Elimination with Matrices
Lecture 3 – Multiplication and Inverse Matrices
Lecture 4 – Factorization into A = LU
Lecture 5 – Transposes, Permutations, Spaces Rn
Lecture 6 – Column Space and Nullspace
Lecture 7 – Solving Ax = 0: Pivot Variables, Special Solutions
Lecture 8 – Solving Ax = b: Row Reduced Form R
Lecture 9 – Independence, Basis, and Dimension
Lecture 10 – The Four Fundamental Subspaces
Lecture 11 – Matrix Spaces; Rank 1; Small World Graphs
Lecture 12 – Graphs, Networks, Incidence Matrices
Lecture 13 – Quiz 1 Review
Lecture 14 – Orthogonal Vectors and Subspaces
Lecture 15 – Projections onto Subspaces
Lecture 16 – Projection Matrices and Least Squares
Lecture 17 – Orthogonal Matrices and Gram-Schmidt
Lecture 18 – Properties of Determinants
Lecture 19 – Determinant Formulas and Cofactors
Lecture 20 – Cramer’s Rule, Inverse Matrix, and Volume
Lecture 21 – Eigenvalues and Eigenvectors
Lecture 22 – Diagonalization and Powers of A
Lecture 23 – Differential Equations and exp(At)
Lecture 24 – Markov Matrices; Fourier Series
Lecture 24b – Quiz 2 Review
Lecture 25 – Symmetric Matrices and Positive Definiteness
Lecture 26 – Complex Matrices; Fast Fourier Transform
Lecture 27 – Positive Definite Matrices and Minima
Lecture 28 – Similar Matrices and Jordan Form
Lecture 29 – Singular Value Decomposition
Lecture 30 – Linear Transformations and Their Matrices
Lecture 31 – Change of Basis; Image Compression
Lecture 32 – Quiz 3 Review
Lecture 33 – Left and Right Inverses; Pseudoinverse
Lecture 34 – Final Course Review