標題: Titlebook: New Foundations in Mathematics; The Geometric Concep Garret Sobczyk Textbook 2013 Springer Science+Business Media New York 2013 Clifford al [打印本頁] 作者: counterfeit 時間: 2025-3-21 18:48
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作者: 修正案 時間: 2025-3-21 23:58 作者: white-matter 時間: 2025-3-22 03:31 作者: Meander 時間: 2025-3-22 04:59
https://doi.org/10.1007/978-0-8176-8385-6Clifford algebra; Lie algebras; geometric algebra; interpolation; linear and multilinear algebra; special作者: 寬大 時間: 2025-3-22 11:43 作者: Congregate 時間: 2025-3-22 13:49 作者: IST 時間: 2025-3-22 18:05
Geometric Algebra,The real number system . has a long and august history spanning a host of civilizations over a period of many centuries [17]. It may be considered the rock upon which many other mathematical systems are constructed and, at the same time, serves as a model of desirable properties that any extension of the real numbers should have.作者: 脖子 時間: 2025-3-22 22:28 作者: 仔細閱讀 時間: 2025-3-23 04:05
Hermitian Inner Product Spaces,In the last chapter, we discovered that the positive definite quadratic form (3.28) used to define the inner product of the Euclidean space ., and the corresponding geometric algebra ., is only one of the many possible quadratic forms. We now introduce the .. of a general .. and the corresponding geometric algebra ..作者: Spinal-Tap 時間: 2025-3-23 08:24
Calculus on ,-Surfaces,We apply all of the machinery of linear algebra developed in the preceding chapters to the study of calculus on an .-surface. The concept of the boundary of a surface is defined, and the classical integration theorems in any dimension follow from a single ..1作者: jarring 時間: 2025-3-23 12:45
Non-euclidean and Projective Geometries,We investigate the relationship between conformal transformations in ., studied in the previous chapter, and orthogonal transformations acting on the . in .. The horosphere is a nonlinear model of a pseudo-Euclidean space in a pseudo-Euclidean space of two dimensions higher.作者: 食品室 時間: 2025-3-23 16:13
Lie Groups and Lie Algebras,We have studied linear transformation on . using the traditional matrix formalism in Chap. 7 and more generally in Chaps. 8–10, using the machinery of geometric algebra. This chapter explains the . interpretation of a general linear operator and offers a new proof of the Cayley–Hamilton theorem based upon this interpretation.作者: ECG769 時間: 2025-3-23 18:22
Vector Spaces and Matrices,a column vector. Since the rules of matrix algebra over the real and complex numbers are identical to the rules of the addition and multiplication of geometric numbers, it makes sense to consider matrices whose entries are geometric numbers alongside the more traditional matrices of real and complex numbers.作者: choleretic 時間: 2025-3-23 23:38 作者: ostracize 時間: 2025-3-24 05:36
Linear Transformations on ,,f geometric algebra, such as the .-derivative and the simplicial .-derivative, are used to study its basic properties. We introduce the adjoint linear transformation and use it to derive the inverse of a nonsingular transformation.作者: 會議 時間: 2025-3-24 06:44
Structure of a Linear Operator,tral basis of idempotents and nilpotents which was developed in Chap. 1 for modular polynomials. The . of a linear operator, while technically more difficult, is just a refinement of its more fundamental spectral decomposition.作者: gregarious 時間: 2025-3-24 12:28
Linear and Bilinear Forms,oint. Instead of talking about the . of a given basis, we introduce the concept of a .. The relationship between a bilinear and a quadratic form is discussed, and Sylvester’s famous law of inertia is proven. The material lays the foundation for studying geometric algebras of arbitrary signatures in later chapters.作者: 離開可分裂 時間: 2025-3-24 17:36 作者: GREEN 時間: 2025-3-24 19:48 作者: FIR 時間: 2025-3-25 02:09 作者: 熒光 時間: 2025-3-25 07:23 作者: 機密 時間: 2025-3-25 11:13 作者: ligature 時間: 2025-3-25 11:38
Outer Product and Determinants,ls in the study of the structure of a linear transformation. A set of vectors is . if and only if the outer product of those vectors is not zero. Whereas a determinant is scalar valued, the outer product characterizes the . of the subspace spanned by the set of vectors.作者: 背景 時間: 2025-3-25 16:36 作者: 中子 時間: 2025-3-25 22:47 作者: Minuet 時間: 2025-3-26 03:04 作者: anticipate 時間: 2025-3-26 06:51
Geometry of Moving Planes, concept of 2-dimensional space–time in the geometric algebra ., introduced in ., generalizes to the full 4-dimensional space–time of special relativity in the geometric algebra .. With only a slight loss of generality, we then restrict our attention to the study of 3-dimensional space–time in the g作者: Muffle 時間: 2025-3-26 10:22 作者: Vertebra 時間: 2025-3-26 12:59 作者: Fillet,Filet 時間: 2025-3-26 16:47 作者: GLOSS 時間: 2025-3-27 00:44 作者: reception 時間: 2025-3-27 01:08
Garret Sobczyktween disciplines and policy-research.Supports dialogue betw.This open access book foregrounds novel collaborations between the Social Sciences and Humanities (SSH), and Science, Technology, Engineering and Mathematics (STEM) disciplines, for the benefit of European energy policy. Each chapter has b作者: gratify 時間: 2025-3-27 05:34 作者: thyroid-hormone 時間: 2025-3-27 09:27
Garret Sobczyk produced cover a diverse range of topics and policy areas and are informed by various interdisciplinary collaborative activities. The outputs of the interdisciplinary collaborations evidence: (1) how questions related to energy supply, demand and systems benefit from both Social Sciences and Humani作者: 高原 時間: 2025-3-27 17:31
Garret Sobczyktween disciplines and policy-research.Supports dialogue betw.This open access book foregrounds novel collaborations between the Social Sciences and Humanities (SSH), and Science, Technology, Engineering and Mathematics (STEM) disciplines, for the benefit of European energy policy. Each chapter has b作者: idiopathic 時間: 2025-3-27 19:56
Garret Sobczyk produced cover a diverse range of topics and policy areas and are informed by various interdisciplinary collaborative activities. The outputs of the interdisciplinary collaborations evidence: (1) how questions related to energy supply, demand and systems benefit from both Social Sciences and Humani作者: NEXUS 時間: 2025-3-27 23:48 作者: 不溶解 時間: 2025-3-28 04:11 作者: ironic 時間: 2025-3-28 09:42 作者: accordance 時間: 2025-3-28 12:01 作者: 尖酸一點 時間: 2025-3-28 15:32 作者: 品牌 時間: 2025-3-28 21:26
Garret Sobczykinto account the following: (1) Using large language models to analyse user-generated content is a reliable methodology for gathering and analysing typically overlooked relevant information regarding citizens‘ perceptions in the implementation of sustainable mobility policies; (2) The substantial pr作者: 吞下 時間: 2025-3-29 00:37 作者: GAVEL 時間: 2025-3-29 07:06
Garret Sobczykinto account the following: (1) Using large language models to analyse user-generated content is a reliable methodology for gathering and analysing typically overlooked relevant information regarding citizens‘ perceptions in the implementation of sustainable mobility policies; (2) The substantial pr作者: Meander 時間: 2025-3-29 09:11 作者: anesthesia 時間: 2025-3-29 11:38 作者: 強化 時間: 2025-3-29 19:28
Garret Sobczyke of interest to anyone developing, implementing or critiquing energy policy (locally, nationally or internationally) as well as those looking to expand the use of interdisciplinary research to achieve sustainability goals.?..Part of a three-volume collection covering climate, energy, and mobility policy..978-3-031-66483-0978-3-031-66481-6作者: Lethargic 時間: 2025-3-29 21:54
Garret Sobczyke of interest to anyone developing, implementing or critiquing energy policy (locally, nationally or internationally) as well as those looking to expand the use of interdisciplinary research to achieve sustainability goals.?..Part of a three-volume collection covering climate, energy, and mobility policy..978-3-031-66483-0978-3-031-66481-6作者: initiate 時間: 2025-3-30 00:25
Garret Sobczykes. Yet, there is the need to consider interdisciplinarity, and what this means in practice, critically. In doing so, it demonstrates the value of focusing more on the interdisciplinary processes and experiences in play. Indeed, across the book chapters, there were commonalities in how the interdisc作者: GIDDY 時間: 2025-3-30 05:41 作者: CURL 時間: 2025-3-30 11:02 作者: 過份艷麗 時間: 2025-3-30 12:55 作者: 一小塊 時間: 2025-3-30 17:35 作者: CHANT 時間: 2025-3-31 00:14 作者: condone 時間: 2025-3-31 03:09 作者: 難聽的聲音 時間: 2025-3-31 07:38 作者: 帳單 時間: 2025-3-31 10:43
Garret Sobczykce recent developments such as ChatGPT allows decision-makers and their teams to rapidly generate and assess a great amount of relevant data. This can facilitate policymakers‘ effectiveness and efficiency in the decision-making processes in urban mobility planning. However, policymakers should be aw作者: Ablation 時間: 2025-3-31 17:19 作者: 審問 時間: 2025-3-31 20:32 作者: Matrimony 時間: 2025-4-1 00:44 作者: frenzy 時間: 2025-4-1 03:54
treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book fo978-0-8176-8385-6作者: Opponent 時間: 2025-4-1 09:42
Textbook 2013h to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of mode作者: Indebted 時間: 2025-4-1 13:48
