Advanced Linear Algebra with Applications
暫譯: 進階線性代數及其應用

Mohammad Ashraf , Vincenzo De Filippis , Mohammad Aslam Siddeeque

Advanced Linear Algebra with Applications
  • 出版商: Springer
  • 出版日期: 2022-04-28
  • 售價: $2,300
  • 貴賓價: 9.5 折 $2,185
  • 語言: 英文
  • 頁數: 511
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 9811621667
  • ISBN-13: 9789811621666
  • 相關分類: 線性代數 Linear-algebra

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

 

This is a comprehensive textbook of linear algebra, intended for advanced undergraduate students of mathematics. Throughout the text, proofs have been made direct and simple without irrelevant details. It needs no prerequisites except some basic knowledge of sets, mappings and number systems. The topics have been presented in a simple and coherent style. The book starts with a quick review of basic literature on groups, rings and fields and ends with the applications of linear algebra in analytical geometry and numerical methods. It also includes a number of exercises and examples at the end of each chapter to enhance the understanding of readers. The subject is developed in a manner accessible to students with little knowledge of linear algebra.

 

Chapters 1-6 discuss introductory topics like groups, rings, fields, matrices, determinants, systems of linear equations, vector spaces, linear transformations, dual spaces, and inner product spaces, which are taught at the first course of linear algebra at the undergraduate level. Chapters 7-9 cover advanced topics like canonical, bilinear, quadratic, sesquilinear and Hermitian forms of operators and matrices, which are taught at the advanced undergraduate course in mathematics. Chapters 10-12 focus on empowering readers to pursue interdisciplinary applications of linear algebra and illustrate the power of the subject through a variety of applications in numerical methods, analytical geometry and in solving linear system of differential equations.

 

商品描述(中文翻譯)

這是一本全面的線性代數教科書，旨在為高年級本科數學學生提供學習資源。全書的證明過程直接且簡單，沒有不相關的細節。除了對集合、映射和數字系統的一些基本知識外，無需任何先修課程。主題以簡單且連貫的風格呈現。書籍開始時快速回顧了群、環和域的基本文獻，並以線性代數在解析幾何和數值方法中的應用作結尾。每章末尾還包括若干練習題和例子，以增強讀者的理解。該主題以易於接觸的方式發展，適合對線性代數知識較少的學生。

第1至第6章討論了入門主題，如群、環、域、矩陣、行列式、線性方程組、向量空間、線性變換、對偶空間和內積空間，這些內容通常在本科線性代數的第一門課程中教授。第7至第9章涵蓋了高級主題，如運算子和矩陣的典範形式、雙線性形式、二次形式、半線性形式和厄米形式，這些內容通常在高年級本科數學課程中教授。第10至第12章專注於使讀者能夠追求線性代數的跨學科應用，並通過數值方法、解析幾何以及解線性微分方程組的各種應用來展示該主題的強大。

作者簡介

MOHAMMAD ASHRAF is Professor at the Department of Mathematics, Aligarh Muslim University, India. He completed his Ph.D. in Mathematics from Aligarh Muslim University, India, in 1986, with the thesis titled "A study of certain commutativity conditions for associative rings". He has authored over 200 research publications in various areas of mathematics such as ring theory, coding theory and graph theory. He is a recipient of the Young Scientist's Award (1988) from Indian Science Congress Association, I.M.S. Prize (1995) from Indian Mathematical Society, and the Ziauddin Gold Medal for securing first position at M.Sc. examination in the year 1981. He is presently dealing with two major research projects awarded by the Department of Science and Technology in the area of derivations in rings. His research interests include ring theory/commutativity and structure of rings and near-rings, derivations on rings, near-rings and Banach algebras, functional identities in rings and algebras, applied linear algebra, algebraic coding theory, cryptography, and graph theory.

VINCENZO DE FILIPPIS is Associate Professor at the Department of Mathematics, University of Messina, Italy. He completed his Ph.D. in Mathematics from the University of Messina, Italy, in 1999 with the thesis titled "Leads in rings first". His research articles have been published in journals and conference proceedings of repute. He is the recipient of the Young Researcher Prize by the University of Messina, Italy, in 2005.

MOHAMMAD ASLAM SIDDEEQUE is Assistant Professor at the Department of Mathematics, Aligarh Muslim University, India. He completed his Ph.D. in Mathematics from Aligarh Muslim University, India, in 2014 with the thesis titled "On derivations and related mappings in rings and near-rings". His area of research includes the study of derivations over rings and near-rings on which he has published research articles in journals of repute.

 

作者簡介(中文翻譯)

MOHAMMAD ASHRAF 是印度阿里格爾穆斯林大學數學系的教授。他於1986年在阿里格爾穆斯林大學獲得數學博士學位，論文題目為「某些關於可交換環的條件研究」。他在環論、編碼理論和圖論等數學各領域發表了超過200篇研究論文。他曾獲得1988年印度科學大會的青年科學家獎、1995年印度數學學會的I.M.S.獎，以及1981年碩士考試中獲得第一名的Ziauddin金獎。他目前正在處理兩個由科學與技術部頒發的主要研究項目，研究主題為環中的導數。他的研究興趣包括環論/可交換性、環和近環的結構、環、近環和巴拿赫代數上的導數、環和代數中的函數恆等式、應用線性代數、代數編碼理論、密碼學和圖論。

VINCENZO DE FILIPPIS 是意大利梅西納大學數學系的副教授。他於1999年在梅西納大學獲得數學博士學位，論文題目為「環中的引導」。他的研究文章已發表在多個知名期刊和會議論文集中。他於2005年獲得意大利梅西納大學的青年研究者獎。

MOHAMMAD ASLAM SIDDEEQUE 是印度阿里格爾穆斯林大學數學系的助理教授。他於2014年在阿里格爾穆斯林大學獲得數學博士學位，論文題目為「環和近環中的導數及相關映射」。他的研究領域包括對環和近環的導數研究，並在多個知名期刊上發表了相關研究文章。

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