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Titlebook: Matrix Groups; Morton L. Curtis Textbook 19791st edition Springer Science+Business Media New York 1979 Groups.Matrizengruppe.algebra.cliff

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書目名稱Matrix Groups
編輯Morton L. Curtis
視頻videohttp://file.papertrans.cn/628/627749/627749.mp4
叢書名稱Universitext
圖書封面Titlebook: Matrix Groups;  Morton L. Curtis Textbook 19791st edition Springer Science+Business Media New York 1979 Groups.Matrizengruppe.algebra.cliff
描述These notes were developed from a course taught at Rice Univ- sity in the spring of 1976 and again at the University of Hawaii in the spring of 1977. It is assumed that the students know some linear algebra and a little about differentiation of vector-valued functions. The idea is to introduce students to some of the concepts of Lie group theory--all done at the concrete level of matrix groups. As much as we could, we motivated developments as a means of deciding when two matrix groups (with different definitions) are isomorphie. In Chapter I "group" is defined and examples are given; ho- morphism and isomorphism are defined. For a field k denotes the algebra of n x n matrices over k We recall that A E Mn(k) has an inverse if and only if det A # 0 , and define the general linear group GL(n,k) We construct the skew-field E of quaternions and note that for A E Mn(E) to operate linearlyon Rn we must operate on the right (since we multiply a vector by a scalar n n on the left). So we use row vectors for Rn, c E and write xA , for the row vector obtained by matrix multiplication. We get a complex-valued determinant function on Mn (E) such that det A # 0 guarantees that A has an inverse.
出版日期Textbook 19791st edition
關(guān)鍵詞Groups; Matrizengruppe; algebra; clifford algebra; field; group theory; homomorphism; lie algebra; lie group
版次1
doihttps://doi.org/10.1007/978-1-4684-0093-9
isbn_ebook978-1-4684-0093-9Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer Science+Business Media New York 1979
The information of publication is updating

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Topology,phisms of groups. So a connected matrix group could not be isomorphic with a nonconnected matrix group, and a similar statement holds for compactness. We will define these properties and decide which of our groups have them. This will be done in sections B and C.
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Topology,pactness, which some of our groups have and others do not. These properties are preserved by continuous maps and so are surely invariants under isomorphisms of groups. So a connected matrix group could not be isomorphic with a nonconnected matrix group, and a similar statement holds for compactness.
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Spin(k),t more groups as subgroups of G. For example, we have used the algebra M.(R) in which the group of units is GL(n,R) and we have the important subgroup SO(n). Our groups Spin(k) are subgroups of the group of units in the Clifford algebra C..
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of MATLAB algorithms.Appendices with all the necessary backg.This is a textbook for undergraduate students of chemical and biological engineering. It is also useful for graduate students, professional engineers and numerical analysts. All reactive chemical and biological processes are highly nonline
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