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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 same definition is used if D is a Cartier divisor on a complete variety over k. [X/G] The quotient stack of, say, an algebraic space X by an action of a group scheme G. / / The GIT quotient of a scheme X by an action of a group scheme G. L n An ambiguous notation.
Geometric algebra (GA) is an extension or completion of vector algebra (VA). [1] The reader is herein assumed to be familiar with the basic concepts and operations of VA and this article will mainly concern itself with operations in the GA of 3D space (nor is this article intended to be mathematically rigorous).
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials ; the modern approach generalizes this in a few different aspects.
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 .
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.
Most contemporary reference works define mathematics by summarizing its main topics and methods: The abstract science which investigates deductively the conclusions implicit in the elementary conceptions of spatial and numerical relations, and which includes as its main divisions geometry, arithmetic, and algebra. [16] Oxford English Dictionary ...
In applied fields the word "tight" is often used with the same meaning. [2] smooth Smoothness is a concept which mathematics has endowed with many meanings, from simple differentiability to infinite differentiability to analyticity, and still others which are more complicated. Each such usage attempts to invoke the physically intuitive notion ...