| 书目名称 | Matrix Groups |
| 编辑 | Morton L. Curtis |
| 视频video | |
| 丛书名称 | Universitext |
| 图书封面 |  |
| 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 isomorphic. 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 lli of to operate linearly on llin quaternions and note that for A E Mn(lli) we must operate on the right (since we mUltiply a vector by a scalar n on the left). So we use row vectors for R , en, llin and write xA for the row vector obtained by matrix multiplication. We get a ~omplex-valued determinant function on Mn (11) such that det A ~ 0 guarantees that A has a |
| 出版日期 | Textbook 1984Latest edition |
| 关键词 | Abelian group; Algebra; Group theory; Groups; Matrizengruppe; Vector space; homomorphism |
| 版次 | 2 |
| doi | https://doi.org/10.1007/978-1-4612-5286-3 |
| isbn_softcover | 978-0-387-96074-6 |
| isbn_ebook | 978-1-4612-5286-3Series ISSN 0172-5939 Series E-ISSN 2191-6675 |
| issn_series | 0172-5939 |
| copyright | Springer-Verlag New York Inc. 1984 |
发表于 2025-3-21 18:53:00
