| 書(shū)目名稱(chēng) | Matrix Groups | | 編輯 | Morton L. Curtis | | 視頻video | http://file.papertrans.cn/628/627749/627749.mp4 | | 叢書(shū)名稱(chēng) | Universitext | | 圖書(shū)封面 |  | | 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 | | doi | https://doi.org/10.1007/978-1-4684-0093-9 | | isbn_ebook | 978-1-4684-0093-9Series ISSN 0172-5939 Series E-ISSN 2191-6675 | | issn_series | 0172-5939 | | copyright | Springer Science+Business Media New York 1979 |
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