geometric algebra in a sentence
1) This result can be generalized to higher dimensions using geometric algebra .
algebra collocations
2) In geometric algebra this vector is classified as a bivector.
3) More generally every real geometric algebra is isomorphic to a matrix algebra.
geometric algebra example sentences
4) They can be associated with bivectors from geometric algebra .5) The geometric interpretation of real Clifford algebras is known as geometric algebra .
6) In geometric algebra (GA) these are multivectors.
7) They are studied in geometric algebra .
8) Other representation comes from the geometric algebra (GA).
9) Unless otherwise stated, this article will treat only nondegenerate geometric algebras .
10) Most instances of geometric algebras of interest have a nondegenerate quadratic form.
11) Geometric algebra can be applied to projective geometry in a straightforward way.
12) An example of geometric algebra would be solving the linear equation ax = bc.
13) The algebra generated by the geometric product is the geometric algebra over the vector space.
14) For this article the bivector will be considered only in real geometric algebras .
15) As has been suggested in earlier sections much of geometric algebra generalises well into higher dimensions.
example sentences with geometric algebra
16) For further detail about the geometrical uses of Clifford algebras, see geometric algebra .17) The "geometrical" approach to geometric algebras has seen a number of 20th-century revivals.
18) A description of the projective geometry can be constructed in the geometric algebra using basic operations.
19) The geometric algebra used is , the algebra of the real vector space R"n".
20) A strong dose of geometric algebra and calculus is the best medicine for both prevention and cure.
21) An introduction to the exterior algebra, and geometric algebra , with a focus on applications.
22) The ancient Greeks made significant advances using geometric algebra , that is solving number problems using geometric processes.
23) There is no unique way to generalize these transformations to the entire geometric algebra without further restriction.
24) In geometric algebra , a rotor and the objects it acts on live in the same space.
25) The formalism of geometric algebra (GA) provides an extension and interpretation of the quaternion method.
26) From the axioms, with closure, every multivector of the geometric algebra is a sum of blades.
27) Every multivector of the geometric algebra can be expressed as a linear combination of the canonical basis elements.
28) Rotors are natural and non-mysterious in geometric algebra and easily understood as the encoding of a double reflection.
How to use geometric algebra in a sentence
29) In computer graphics and robotics, geometric algebras have been revived in order to efficiently represent rotations and other transformations.30) For example, __FORMULA__ models 3D Euclidean space, __FORMULA__ relativistic spacetime and __FORMULA__ a 3D conformal geometric algebra .
31) This formalism is used in geometric algebra and, more generally, in the Clifford algebra representation of Lie groups.
32) Indeed, the use of geometric algebra in Computer-Aided geometric Design, Computer Vision and robotics is expanding rapidly.
33) This can be done using geometric algebra , with the planes of rotations associated with simple bivectors in the algebra.
34) Moreover, it is demonstrated that every linear transformation can be represented as a monomial of vectors in geometric algebra .
35) The geometric algebra of an "n"-dimensional vector space is spanned by 2"n" canonical basis elements.
36) It is naturally described if using geometric algebra and bivectors, with the Euclidean metric replaced by a Minkowski metric.
37) But given the simple bivectors geometric algebra is a useful tool for studying planes of rotation using algebra like the above.
38) The basic multiplication in the geometric algebra is the geometric product, denoted by simply juxtaposing two vectors as in ab.
39) In 1957, Artin wrote a book on geometric algebra an insightful development of the classical groups in a Kleinian context.
40) Elements of the geometric algebra that are simply scalar multiples of 1 are grade-0 blades and are called "scalars".
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