Abstract
With his theory of extensions Hermann Grassmann gave algebra a substantial different shape: He indeed had invented a generalized version of Pauli and Dirac Algebra which can be applied not only to re-model our mathematical view on space and time, but also to re-model mathematics – and especially the relation between geometry and algebra – itself. Therefore this didactical version of generalized Pauli and Dirac Algebra is called Geometric Algebra.In the following an introduction to Geometric Algebra is given and applications of Geometric Algebra in physics and mathematics are discussed. Special emphasis is given to the mathematics of pure and mixed sandwich products and to a different view on solving systems of linear equations. At the end matrix inverses of non-square matrices (e.g. Moore-Penrose generalized inverses) are discussed.
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