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From Vectors to Multivectors (Part 1 of 3)
Introduced by Hermann Grassmann and greatly expanded by William Kingdon Clifford during the 19th century, Geometric Algebras provide a proper abstract framework for the treatment of geometrical vector operations that extend naturally to general dimensions. Their concise concepts yield elegant and peculiarly coherent constructs, in contrast with the intricacies of Vector Calculus. Because of the geometric origin of their structures and close relation to quadratic forms they turn useful in a wide range of applications in theoretical and applied sciences across several fields.
Macdonald A. Linear and Geometric Algebra
CreateSpace Independent Publishing Platform, Springer, ISBN This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations. The text is divided into two parts: part one focuses on complex analysis and part two on Wiley,
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This textbook for the second year undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most of the usual linear algebra topics. Geometric algebra and its extension to geometric calculus simplify, unify, and generalize vast areas of mathematics that involve geometric ideas. Geometric algebra is an extension of linear algebra. The treatment of many linear algebra topics is enhanced by geometric algebra, for example, determinants and orthogonal transformations. And geometric algebra does much more, as it incorporates the complex, quaternion, and exterior algebras, among others.