Invited Talks

Tim Clark, William W. Cohen, Lawrence Hunter, Chris J. Lintott, Jude W. Shavlik
{"title":"Invited Talks","authors":"Tim Clark, William W. Cohen, Lawrence Hunter, Chris J. Lintott, Jude W. Shavlik","doi":"10.1109/SC.1998.10012","DOIUrl":null,"url":null,"abstract":": If we graph the simplest quadratic, we see that its range, or its image, consists of all positive numbers and zero. Let us extend this idea by instead evaluating polynomials on square matrices whose entries come from the complex numbers. A version of the L'vov-Kaplansky conjecture states that the image of a multilinear polynomial evaluated over matrices, with entries from the complex numbers, is a vector space, which is an algebraic structure that much is known about. We will consider this problem in a slightly different context by adding in some elements to the complex numbers that are not necessarily commutative. We will see how the existence of such elements changes the structure of our polynomials and their images. The talk will be accessible to anyone interested in mathematics.","PeriodicalId":426921,"journal":{"name":"2022 International Conference on Breakthrough in Heuristics And Reciprocation of Advanced Technologies (BHARAT)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"22","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2022 International Conference on Breakthrough in Heuristics And Reciprocation of Advanced Technologies (BHARAT)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SC.1998.10012","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 22

Abstract

: If we graph the simplest quadratic, we see that its range, or its image, consists of all positive numbers and zero. Let us extend this idea by instead evaluating polynomials on square matrices whose entries come from the complex numbers. A version of the L'vov-Kaplansky conjecture states that the image of a multilinear polynomial evaluated over matrices, with entries from the complex numbers, is a vector space, which is an algebraic structure that much is known about. We will consider this problem in a slightly different context by adding in some elements to the complex numbers that are not necessarily commutative. We will see how the existence of such elements changes the structure of our polynomials and their images. The talk will be accessible to anyone interested in mathematics.
邀请谈判
如果我们画出最简单的二次型,我们会看到它的范围,或者它的像,由所有正数和零组成。让我们扩展这个思想,代之以求项来自复数的方阵上的多项式。L'vov-Kaplansky猜想的一个版本指出,一个多元线性多项式的图像在矩阵上求值,其元素来自复数,是一个向量空间,这是一个众所周知的代数结构。我们将在稍微不同的背景下考虑这个问题,在复数中加入一些不一定可交换的元素。我们将看到这些元素的存在如何改变多项式及其图像的结构。任何对数学感兴趣的人都可以参加这次演讲。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信