Titlebook: New Foundations in Mathematics; The Geometric Concep Garret Sobczyk Textbook 2013 Springer Science+Business Media New York 2013 Clifford al

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https://doi.org/10.1007/978-0-8176-8385-6Clifford algebra; Lie algebras; geometric algebra; interpolation; linear and multilinear algebra; special

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Geometric Algebra,The real number system . has a long and august history spanning a host of civilizations over a period of many centuries [17]. It may be considered the rock upon which many other mathematical systems are constructed and, at the same time, serves as a model of desirable properties that any extension of the real numbers should have.

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Hermitian Inner Product Spaces,In the last chapter, we discovered that the positive definite quadratic form (3.28) used to define the inner product of the Euclidean space ., and the corresponding geometric algebra ., is only one of the many possible quadratic forms. We now introduce the .. of a general .. and the corresponding geometric algebra ..

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Calculus on ,-Surfaces,We apply all of the machinery of linear algebra developed in the preceding chapters to the study of calculus on an .-surface. The concept of the boundary of a surface is defined, and the classical integration theorems in any dimension follow from a single ..1