Steven J. Rosenberg
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引用次数: 0

摘要

群是一个运算的基本代数结构。在这本书中,分组出现在许多上下文中。例如,在第2-5章中介绍的所有信号域都具有可加交换群的结构。同时,域和信号的变换集合具有非交换群的结构。这在第12章中被广泛使用。本附录提供了群的基本定义和性质,但任何关于抽象代数的标准文本都应该参考更详细的处理,例如,Dummit和Foote(2004)的第一部分或Miller(1972)的第1章。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
GROUPS
The group is the basic algebraic structure with one operation. Groups appear in many contexts in this book. For example, all the signal domains introduced in Chapters 2–5 have the structure of an additive commutative group. Also, sets of transformations of domains and signals have the structure of a noncommutative group. This is used extensively in Chapter 12. This appendix provides basic definitions and properties of groups, but any standard text on abstract algebra should be consulted for a more detailed treatment, e.g, part I of Dummit and Foote (2004) or chapter 1 of Miller (1972).
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