Introduction to Matrix Theory
暫譯: 矩陣理論導論

Singh, Arindama

Introduction to Matrix Theory
  • 出版商: Springer
  • 出版日期: 2021-08-17
  • 售價: $3,680
  • 貴賓價: 9.5 折 $3,496
  • 語言: 英文
  • 頁數: 194
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3030804801
  • ISBN-13: 9783030804800

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商品描述

This book is designed to serve as a textbook for courses offered to undergraduate and postgraduate students enrolled in Mathematics. Using elementary row operations and Gram-Schmidt orthogonalization as basic tools the text develops characterization of equivalence and similarity, and various factorizations such as rank factorization, OR-factorization, Schurtriangularization, Diagonalization of normal matrices, Jordan decomposition, singular value decomposition, and polar decomposition. Along with Gauss-Jordan elimination for linear systems, it also discusses best approximations and least-squares solutions. The book includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix. The topics in the book are dealt with in a lively manner. Each section of the book has exercises to reinforce the concepts, and problems have been added at the end of each chapter. Most of these problems are theoretical, and they do not fit into the running text linearly. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in senior undergraduate and beginning postgraduate mathematics courses.

商品描述(中文翻譯)

本書旨在作為數學本科生和研究生課程的教科書。使用基本的行運算和 Gram-Schmidt 正交化作為基本工具，文本發展了等價性和相似性的特徵，以及各種因式分解，如秩因式分解（rank factorization）、OR-因式分解、Schur 三角化、正常矩陣的對角化、Jordan 分解、奇異值分解（singular value decomposition）和極分解（polar decomposition）。除了針對線性系統的高斯-喬丹消去法（Gauss-Jordan elimination），本書還討論了最佳近似和最小二乘解。書中包括矩陣的範數作為處理線性系統迭代解和矩陣指數的手段。書中的主題以生動的方式進行探討。每個章節都有練習題以加強概念，並在每章的末尾添加了問題。這些問題大多是理論性的，並不會線性地融入文本中。詳細的內容涵蓋和教學工具使本書成為高年級本科生和初級研究生數學課程的理想教科書。

作者簡介

Dr. Arindama Singh is currently a Professor at the Department of Mathematics, Indian Institute of Technology Madras, India. He has 31 years of teaching and research experience. He has guided 5 Ph.D., 4 M.Phil., and 18 M.Sc. students. He has published 5 books, over 50 papers in refereed Journals, and 10 conference proceedings. He also has written some expository papers in basic mathematics. His areas of interest are the numerical solution of singularly perturbed differential equations (NSSPTPBVS), knowledge compilation, numerical solution of singularly perturbed elliptic problems (NSSPEP), image restoration, and mathematical learning theory.

作者簡介(中文翻譯)

阿林達瑪·辛格博士目前是印度馬德拉斯印度理工學院數學系的教授。他擁有31年的教學和研究經驗，指導過5位博士生、4位碩士研究生及18位碩士生。他已出版5本書籍，並在同行評審的期刊上發表了超過50篇論文，以及10篇會議論文。他還撰寫了一些有關基礎數學的說明性論文。他的研究興趣包括奇異擾動微分方程的數值解（NSSPTPBVS）、知識編譯、奇異擾動橢圓問題的數值解（NSSPEP）、影像修復以及數學學習理論。

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