標(biāo)題: Titlebook: Applications of Geometric Algebra in Computer Science and Engineering; Leo Dorst,Chris Doran,Joan Lasenby Book 2002 Springer Science+Busin [打印本頁] 作者: 動詞 時間: 2025-3-21 19:11
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作者: APNEA 時間: 2025-3-21 20:42
https://doi.org/10.1007/978-1-4020-8265-8ann ’s Ausdehnungslehre described just such a metricfree geometric algebra of points. However, Whitehead’s treatise spoiled the natural simplicity of the theory by a lopsided derivation based purely on points which gave rise to two different products (progressive and regressive). The current paper t作者: 斥責(zé) 時間: 2025-3-22 02:23 作者: cogitate 時間: 2025-3-22 07:42
Anne L. C. Runehov,Lluis Oviedoee versions: ., which features inner products and outer products of multivectors; ., which features pseudoscalars and inner products of vectors; ., which features geometric products of vectors and multivectors.作者: Fierce 時間: 2025-3-22 12:07
Encyclopedia of Sciences and Religionses operate by left multiplication onto real three-dimensional column vectors; the space of such vectors is the . of the representation. Rotations in different planes do not generally commute, and a common problem considered in texts is how to express the product of given rotations as a single rotati作者: tooth-decay 時間: 2025-3-22 15:48 作者: 匍匐前進(jìn) 時間: 2025-3-22 19:29
https://doi.org/10.1007/978-1-4020-8265-8sented by the .th compound matrix of the .-by-. matrix . := [.., ?, ..] ∈ F. relative to the basis {.., .., ?, ..} 2254; 1, .., ?, ..Λ?Λ..} of the underlying Grassmann algebra ..(F). Since the Clifford product ● is related to the Grassmann product A via . ● . = . Λ . + ..., ., . ∈ F., the question o作者: MIRE 時間: 2025-3-22 22:44
Anne L. C. Runehov,Lluis Oviedolection of abstract K-dimensional cells, k = 0,1,...,n that are assembled into an oriented cellular structure called a starplex and shown in Figure 11.1. The starplex structure represents the combinatorial neighborhood (a star) of a 0-cell in any n-dimensional cell complex representing a typical coo作者: integrated 時間: 2025-3-23 05:25 作者: Fantasy 時間: 2025-3-23 08:23 作者: PHON 時間: 2025-3-23 11:02
Giacomo Rizzolatti,Maria Alessandra Umiltànsion of the program SymbolicC++ by Tan and Steeb and follows their methods of supporting a class through template classes. Classes have been written and tested including Clifford(2), Clifford (3) and Clifford(2,2). The classes can also be accessed from within an interpreted language, Tcl, via an in作者: 斜坡 時間: 2025-3-23 13:56
Encyclopedia of Sciences and Religionsand in particular Ablamowicz [.] gives examples of derivation of the matrix representation. A matrix will itself satisfy the characteristic polynomial equation obeyed by its own eigenvalues. This relationship can be used to calculate the inverse of a matrix from powers of the matrix itself. It is de作者: 自制 時間: 2025-3-23 19:15
Matthew Collins,Beatrice Demarchihave used the insights provided by this work to create a computer program that allows a user to design, modify and visualize a 2D vector field in real time. The vector field is polynomial over the complex field C, and is therefore more computationally efficient and stable than Polya’s rational versi作者: 勾引 時間: 2025-3-23 22:46
Constantine (Dean) K. Christakos bilinear form B such that B(xy, z) = B(x, yz) for all x, y, z ? A, then the maps . → ..(.) and . → ..(.) give inclusion preserving bijections between lattices of left and right ideals of . satisfying(a) Ann.(.. + ..) = ..(..) ? ..(..),..(.. ? ..) = ..(..) + ..(..)(b) ..(.. + ..) = ..(..) ? ..(..),.作者: 背景 時間: 2025-3-24 05:05 作者: 側(cè)面左右 時間: 2025-3-24 08:46
Anne L. C. Runehov,Lluis Oviedoee versions: ., which features inner products and outer products of multivectors; ., which features pseudoscalars and inner products of vectors; ., which features geometric products of vectors and multivectors.作者: 失誤 時間: 2025-3-24 10:41
Giacomo Rizzolatti,Maria Alessandra Umiltànsion of the program SymbolicC++ by Tan and Steeb and follows their methods of supporting a class through template classes. Classes have been written and tested including Clifford(2), Clifford (3) and Clifford(2,2). The classes can also be accessed from within an interpreted language, Tcl, via an interface program.作者: sebaceous-gland 時間: 2025-3-24 18:52
Encyclopedia of Sciences and ReligionsGeometric algebra provides the essential foundation for a new approach to symmetry groups. Each of the 32 lattice point groups and 230 space groups in three dimensions is generated from a set of three .. This greatly facilitates representation, analysis and application of the groups to molecular modeling and crystallography.作者: GROSS 時間: 2025-3-24 21:32 作者: 無彈性 時間: 2025-3-24 23:43
Encyclopedia of Sciences and ReligionsIn this paper we outline several ideas of how to define analysis starting from the algebra of abstract vector variables.作者: 救護(hù)車 時間: 2025-3-25 03:44 作者: Offset 時間: 2025-3-25 09:58
Point Groups and Space Groups in Geometric AlgebraGeometric algebra provides the essential foundation for a new approach to symmetry groups. Each of the 32 lattice point groups and 230 space groups in three dimensions is generated from a set of three .. This greatly facilitates representation, analysis and application of the groups to molecular modeling and crystallography.作者: 不吉祥的女人 時間: 2025-3-25 13:19
Geometric and Algebraic Canonical FormsWe describe some of the applications of Finite Geometry to Clifford Algebras, and then look in more detail at some of the relations between geometrical and algebraic canonical forms. Much of this latter work has been investigated using computer algebra systems, and we include some details of this, along with some of the issues that arise.作者: 倒轉(zhuǎn) 時間: 2025-3-25 18:08 作者: Aggregate 時間: 2025-3-25 22:15 作者: 淺灘 時間: 2025-3-26 02:53 作者: isotope 時間: 2025-3-26 07:54
978-1-4612-6606-8Springer Science+Business Media New York 2002作者: ADJ 時間: 2025-3-26 11:40
http://image.papertrans.cn/a/image/159450.jpg作者: 極為憤怒 時間: 2025-3-26 13:03 作者: 蚊帳 時間: 2025-3-26 18:29 作者: 不妥協(xié) 時間: 2025-3-27 00:23
Symbolic Processing of Clifford Numbers in C++nsion of the program SymbolicC++ by Tan and Steeb and follows their methods of supporting a class through template classes. Classes have been written and tested including Clifford(2), Clifford (3) and Clifford(2,2). The classes can also be accessed from within an interpreted language, Tcl, via an interface program.作者: 燦爛 時間: 2025-3-27 03:04 作者: prick-test 時間: 2025-3-27 05:19 作者: ELATE 時間: 2025-3-27 10:44 作者: Uncultured 時間: 2025-3-27 14:09
Annihilators of Principal Ideals in the Grassmann Algebra lattices of left and right ideals of . satisfying(a) Ann.(.. + ..) = ..(..) ? ..(..),..(.. ? ..) = ..(..) + ..(..)(b) ..(.. + ..) = ..(..) ? ..(..),..(.. ? ..) = ..(..) + ..(..)(c) ..(..(.)) = .and..(..(.)) = ..(For example see [2].)作者: 不合 時間: 2025-3-27 19:10
Unification of Grassmann’s Progressive and Regressive Products using the Principle of Dualityidies up the theory by invoking the principle of duality to put points and hyperplanes on an equal footing and then shows that the theory has just a single antisymmetric product which evaluates to give the same results as Whitehead’s progressive and regressive products.作者: CHARM 時間: 2025-3-27 22:57
From Unoriented Subspaces to Blade Operatorsn technique (a LIFT to a different metric) is presented that makes solutions of some problems translatable from one metric to another. In particular this makes the meet and join computable regardless of incidence properties and even in degenerate metrics.作者: linear 時間: 2025-3-28 04:39
A Multivector Data Structure for Differential Forms and Equationsrdinate control element (usually cubical or simplicial). The combinatorics of the starplex matches exactly the combinatorial structure of the multivector: every oriented k-cell in the starplex corresponds to some basis K-vector.作者: 路標(biāo) 時間: 2025-3-28 08:57
Imaginary Eigenvalues and Complex Eigenvectors Explained by Real Geometryd as rotation operators, which rotate the underlying vector duplets. The second part of this paper extends and generalizes the treatment to three dimensions. Finally the four-dimensional problem is stated.作者: 乳汁 時間: 2025-3-28 10:28 作者: 草率女 時間: 2025-3-28 17:46
A Toy Vector Field Based on Geometric Algebraon over C, which is the traditional approach for such work. Such “toy” vector fields are useful for instruction, understanding and topological simulation of many issues associated with all vector fields.作者: alliance 時間: 2025-3-28 22:45 作者: faction 時間: 2025-3-29 02:33 作者: dithiolethione 時間: 2025-3-29 05:20
Compound Matrices and Pfaffians: A Representation of Geometric Algebracertain matrices which can be understood as the skew symmetric counterpart of the corresponding Gramians. Based on this representation we calculate the .th Clifford power . of a vector . ∈ .. which enables the extension of an analytical function . : . → . to their corresponding Clifford function .:.. → ..(.).作者: Generosity 時間: 2025-3-29 10:43
Jet Bundles and the Formal Theory of Partial Differential Equationsathematical underpinnings of involution (which lie in the theory of combinatorial decompositions of polynomial modules [.,.]) nor other applications of the theory of jet bundles such as the theory of symmetries of systems of PDEs [.] or discretisation schemes based on discrete approximations to jet bundles [.].作者: comely 時間: 2025-3-29 15:28 作者: 自然環(huán)境 時間: 2025-3-29 16:10 作者: 親密 時間: 2025-3-29 21:37
Anne L. C. Runehov,Lluis Oviedordinate control element (usually cubical or simplicial). The combinatorics of the starplex matches exactly the combinatorial structure of the multivector: every oriented k-cell in the starplex corresponds to some basis K-vector.作者: Charitable 時間: 2025-3-30 03:36 作者: CARK 時間: 2025-3-30 05:53
Encyclopedia of Sciences and Religionsmonstrated that the matrix basis of a Clifford number can be used to calculate the inverse of a Clifford number using the characteristic equation of the matrix and powers of the Clifford number. Examples are given for the algebras Clifford(2), Clifford(3) and Clifford(2,2).作者: Resistance 時間: 2025-3-30 11:47
Matthew Collins,Beatrice Demarchion over C, which is the traditional approach for such work. Such “toy” vector fields are useful for instruction, understanding and topological simulation of many issues associated with all vector fields.作者: CHIDE 時間: 2025-3-30 16:06
Encyclopedia of Sciences and Religions? .(2). The carrier spaces of irreducible representations of . (3) comprise complex two-component .. The spinors and their Hermitian conjugates carry two linearly independent irreducible representations, and the vectors of physical space can be expressed as linear combinations of their products.作者: Dissonance 時間: 2025-3-30 18:41
Encyclopedia of Sciences and Religionsas also introduced an improved algorithm in the appendix of [.] to deal with the case for which there are multiple roots in the minimal polynomical for the linear operator. In this paper we will carry this slightly further to obtain an explicit formula for the projection operators.作者: Spinal-Tap 時間: 2025-3-30 23:56 作者: Processes 時間: 2025-3-31 01:53
Functions of Clifford Numbers or Square Matricesas also introduced an improved algorithm in the appendix of [.] to deal with the case for which there are multiple roots in the minimal polynomical for the linear operator. In this paper we will carry this slightly further to obtain an explicit formula for the projection operators.作者: 法律的瑕疵 時間: 2025-3-31 06:14
The Inner Products of Geometric Algebrasitates a slightly different inner product than usual. We demonstrate the use and geometric significance of this ., and show how it simplifies treatment of meet and join. We also derive the sufficient condition for covariance of expressions involving outer and inner products.作者: 樹上結(jié)蜜糖 時間: 2025-3-31 10:48
Unification of Grassmann’s Progressive and Regressive Products using the Principle of Dualityann ’s Ausdehnungslehre described just such a metricfree geometric algebra of points. However, Whitehead’s treatise spoiled the natural simplicity of the theory by a lopsided derivation based purely on points which gave rise to two different products (progressive and regressive). The current paper t作者: 收養(yǎng) 時間: 2025-3-31 15:42 作者: 開始從未 時間: 2025-3-31 17:33
