Basic linear algebra is a branch of mathematics that focuses on solving systems of linear equations using matrix operations. The course will normally evolve from numbers to vectors to subspaces. It is an extremely useful area of mathematics. As pointed out in the preface of Gilbert Strang's Introduction to Linear Algebra, the speed of every new supercomputer is tested on the matrix equation Ax = b. (In case you're interested, the world speed record of 10^15 operations per second was set in 2008 by teams at IBM and Los Alamos.)

A solid introductory course in linear algebra will normally cover the following topics:

- Introduction to vectors
- Solving linear equations
- Vector spaces and subspaces
- Orthogonality
- Determinants
- Eigenvalues and Eigenvectors
- Linear transformations
- Applications
- Numerical linear algebra
- Complex vectors and matrices

A nice set of class notes as well as an eBook in linear algebra is available as a linear algebra tutorial, made possible by professor Paul Dawkins at Lamar University. If you visited the 24HourAnswers.com Matlab subject page, you already know how useful MATLAB is for many types of mathematical calculations. There is a MATLAB tutorial in linear algebra that is quite nice for beginners. For those advanced students, follow the publication called Linear Algebra and its Applications.

Perhaps the most useful online academic resource is MIT's OpenCourseWare. If you are ready to learn linear algebra, go to their online linear algebra course.

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