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Geometric Algebra is a book written by Emil Artin and published by Interscience Publishers, New York, in 1957. It was republished in 1988 in the Wiley Classics series (ISBN 0-471-60839-4). In 1962 Algèbre Géométrique, a translation into French by Michel Lazard, was published by Gauthier-Villars, and reprinted in 1996.
In mathematics, a geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication of vectors results in higher-dimensional objects called multivectors ...
The three books were published by W. H. Freeman and Company, and "overhead transparencies for" classroom use were subsequently developed. [15] The Elementary Algebra text has attracted interest by homeschoolers, particularly when used in conjunction with an independently produced set of DVDs offering 36 hours of educational instruction. [2]
The algebra generated by the geometric product (that is, all objects formed by taking repeated sums and geometric products of scalars and vectors) is the geometric algebra over the vector space. For an Euclidean vector space, this algebra is written G n {\displaystyle {\mathcal {G}}_{n}} or Cl n ( R ) , where n is the dimension of the vector ...
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The universal geometric algebra (n, n) of order 2 2n is defined as the Clifford algebra of 2n-dimensional pseudo-Euclidean space R n, n. [1] This algebra is also called the "mother algebra". It has a nondegenerate signature. The vectors in this space generate the algebra through the geometric product.
Geometric invariant theory was founded and developed by Mumford in a monograph, first published in 1965, that applied ideas of nineteenth century invariant theory, including some results of Hilbert, to modern algebraic geometry questions. (The book was greatly expanded in two later editions, with extra appendices by Fogarty and Mumford, and a ...
In mathematics, geometric calculus extends geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to reproduce other mathematical theories including vector calculus , differential geometry , and differential forms .