Linear Algebra is a core body of mathematics studying vector spaces and linear mappings between these spaces. Key topics include: matrices, vectors, simultaneous systems of linear equations, diagonal form, eigenvalues, eigenvectors, projections, points, lines, planes, hyperplanes, rotations and reflections.

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Being a practicing programmer, you are very unlikely to implement yet another linear system solving algorithm. This introduction doesn't cover the implementation details of such, therefore. Although, you will probably face the problems that may be solved in a form of linear systems, and often more elegantly than by any other means. This tutorial is all about the concepts that should help you recognize these problems and find the best solution for them.