| 书目名称 | Finitely Generated Abelian Groups and Similarity of Matrices over a Field | | 编辑 | Christopher Norman | | 视频video | | | 概述 | The theory of finitely generated abelian groups is introduced in an understandable and concrete way.The analogous theory of similarity of square matrices over a field, including the Jordan form, is ex | | 丛书名称 | Springer Undergraduate Mathematics Series | | 图书封面 |  | | 描述 | .At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version of the Euclidean algorithm and is exactly what the theory requires in both cases. Starting with matrices over the integers, Part 1 of this book provides a measured introduction to such groups: two finitely generated abelian groups are isomorphic if and only if their invariant factor sequences are identical. The analogous theory of matrix similarity over a field is then developed in Part 2 starting with matrices having polynomial entries: two matrices over a field are similar if and only if their rational canonical forms are equal. Under certain conditions each matrix is similar to a diagonal or nearly diagonal matrix, namely its Jordan form.. .The reader is assumed to be familiar with the elementary properties of rings and fields. Also a knowledge of abstract linear algebra including vector spaces, linear mappings, matrices, bases and dimension is essential, although much of the theory is covered in the text but from a more general standpoint: the role of | | 出版日期 | Textbook 2012 | | 关键词 | Abelian groups; Smith normal form; equivalent matrices; homomorphisms and isomorphisms; invariant factor | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4471-2730-7 | | isbn_softcover | 978-1-4471-2729-1 | | isbn_ebook | 978-1-4471-2730-7Series ISSN 1615-2085 Series E-ISSN 2197-4144 | | issn_series | 1615-2085 | | copyright | Springer-Verlag London Limited 2012 |
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发表于 2025-3-21 17:22:14
