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Titlebook: Matrix Groups; An Introduction to L Andrew Baker Textbook 2002 Springer-Verlag London 2002 Group theory.Lie group.Lie groups.Matrix.Matrix

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發(fā)表于 2025-3-21 19:46:25 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Matrix Groups
副標(biāo)題An Introduction to L
編輯Andrew Baker
視頻videohttp://file.papertrans.cn/628/627747/627747.mp4
概述Only introduction to Lie group theory aimed at the undergraduate.Discusses applications in mathematics and physics.Provides a self-contained introduction to Lie groups and serves as a foundation for a
叢書名稱Springer Undergraduate Mathematics Series
圖書封面Titlebook: Matrix Groups; An Introduction to L Andrew Baker Textbook 2002 Springer-Verlag London 2002 Group theory.Lie group.Lie groups.Matrix.Matrix
描述Aimed at advanced undergraduate and beginning graduate students, this book provides a first taste of the theory of Lie groups as an appetiser for a more substantial further course. Lie theoretic ideas lie at the heart of much of standard undergraduate linear algebra and exposure to them can inform or motivate the study of the latter..The main focus is on matrix groups, i.e., closed subgroups of real and complex general linear groups. The first part studies examples and describes the classical families of simply connected compact groups. The second part introduces the idea of a lie group and studies the associated notion of a homogeneous space using orbits of smooth actions..Throughout, the emphasis is on providing an approach that is accessible to readers equipped with a standard undergraduate toolkit of algebra and analysis. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully developed theory, preparing students for a more standard and abstract course in Lie theory and differential geometry..
出版日期Textbook 2002
關(guān)鍵詞Group theory; Lie group; Lie groups; Matrix; Matrix groups; algebra; differential geometry; linear algebra;
版次1
doihttps://doi.org/10.1007/978-1-4471-0183-3
isbn_softcover978-1-85233-470-3
isbn_ebook978-1-4471-0183-3Series ISSN 1615-2085 Series E-ISSN 2197-4144
issn_series 1615-2085
copyrightSpringer-Verlag London 2002
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沙發(fā)
發(fā)表于 2025-3-21 23:21:26 | 只看該作者
板凳
發(fā)表于 2025-3-22 03:17:14 | 只看該作者
Real and Complex Matrix Groups(the complex numbers), however the general framework of this chapter is applicable to more general fields equipped with suitable norms in place of the absolute value. Indeed, as we will see in Chapter 4, much of it even applies to the case of a general . or ., with the . providing the most important
地板
發(fā)表于 2025-3-22 08:21:39 | 只看該作者
Exponentials, Differential Equations and One-parameter Subgroups theory, particularly the .. Indeed, the . provides the link between the . of a matrix group and the group itself. In the case of a compact connected matrix group, the exponential is even surjective, allowing a parametrisation of such a group by a region in ?. for some .; see Chapter 10 for details.
5#
發(fā)表于 2025-3-22 09:42:03 | 只看該作者
Tangent Spaces and Lie Algebras; the definition and basic properties of Lie algebra are introduced in Section 3.1. Amazingly, the Lie algebra of . captures enough of the properties of . to act as a more manageable substitute for many purposes, at least when . is .. The geometric aspects of this will be studied in Chapter 7 when w
6#
發(fā)表于 2025-3-22 16:46:35 | 只看該作者
7#
發(fā)表于 2025-3-22 18:24:45 | 只看該作者
Clifford Algebras and Spinor Groups& Shapiro [3]; Porteous [23, 24] also provides an accessible description, as does Curtis [7] but there are some errors and omissions in that account. Lawson & Michelsohn [19] provides a more sophisticated introduction which shows how central Clifford algebras have become to modern geometry and topol
8#
發(fā)表于 2025-3-22 23:32:09 | 只看該作者
Lorentz Groupsdetails, leaving the reader to fill in the more obvious gaps. The most important example is that for which . = 3 as this provides the geometric setting for Special Relativity. However, many of the main features can be seen in the cases . = 1,2.
9#
發(fā)表于 2025-3-23 04:49:48 | 只看該作者
Lie Groups[6, 8, 29] while [7, 23] contain briefer introductions. One of our main aims is to prove that every matrix subgroup of GL.(?) is a . and we follow the proof of this result described in Howe [12]. We will also show that not every Lie group is a matrix group by exhibiting the simplest counterexample.
10#
發(fā)表于 2025-3-23 06:46:31 | 只看該作者
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