Matrix Theory: Basic Results and Techniques
暫譯: 矩陣理論：基本結果與技術

Zhang, Fuzhen

Matrix Theory: Basic Results and Techniques
  • 出版商: Springer
  • 出版日期: 2026-04-17
  • 售價: $3,060
  • 貴賓價: 9.5 折 $2,907
  • 語言: 英文
  • 頁數: 505
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 1071652370
  • ISBN-13: 9781071652374
  • 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

The aim of this text is to present fundamental ideas, results, and techniques concisely, mainly in matrix theory with some in linear algebra. The book contains ten chapters covering various topics ranging from rank, similarity, and special matrices, to Schur complements, matrix normality, and majorization. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. Major changes in this third edition include:

    expansion of topics such as eigenvalue continuity, matrix functions, nonnegative matrices, matrix norms, and majorization inclusion of more than 200 examples and more than 1500 exercises emphasis on basic techniques and skills for partitioned matrices through which a variety of matrix results and matrix inequalities are shown showcase of many majorization-type inequalities for diagonal entries, eigenvalues, and singular values of matrices.
This book can be used as a textbook or a supplement for a linear algebra and matrix theory class or a seminar for advanced undergraduate or graduate students. Prerequisites include a solid background in elementary linear algebra and calculus. The text can also serve as a reference for researchers in algebra, matrix analysis, operator theory, statistics, computer science, engineering, operations research, economics, and other scientific areas.

From reviews of the second edition:

The author has made a valuable contribution to the textbook literature on matrix theory, and his work will be appreciated by students and teachers of the subject. ... is recommended reading for all those wishing to acquaint themselves with basic matrix theory.-- Vicenţiu D. Rădulescu, Zentralblatt MATH

In many places several different proofs are presented for a theorem. This causes the book to be very attractive and readable. This book is useful for researchers as well as graduate students working in linear algebra, operator theory, statistics, computer science, engineering, applied mathematics, economics, and other disciplines.
-- Mohammad Sal Moslehian, Mathematical Reviews

商品描述(中文翻譯)

本書的目的是簡明扼要地介紹基本概念、結果和技術，主要集中在矩陣理論，並涵蓋一些線性代數的內容。該書包含十個章節，涵蓋從秩、相似性和特殊矩陣，到舒爾補矩陣、矩陣正態性和主導化等各種主題。每個章節專注於美麗、有趣且具代表性的結果、技術和方法，並附有精心挑選的問題。本第三版的主要變更包括：

- 擴展了特徵值連續性、矩陣函數、非負矩陣、矩陣範數和主導化等主題
- 包含超過200個例子和超過1500個練習題
- 強調分區矩陣的基本技術和技能，通過這些技術展示各種矩陣結果和矩陣不等式
- 展示許多針對矩陣對角元素、特徵值和奇異值的主導化類型不等式

本書可作為線性代數和矩陣理論課程的教科書或補充教材，適合高年級本科生或研究生的研討會。先修課程包括扎實的初級線性代數和微積分背景。該文本也可作為代數、矩陣分析、算子理論、統計學、計算機科學、工程、運籌學、經濟學及其他科學領域研究人員的參考資料。

來自第二版的評價：

作者對矩陣理論的教科書文獻做出了寶貴的貢獻，他的作品將受到該主題學生和教師的讚賞。... 是所有希望了解基本矩陣理論的人的推薦讀物。-- Vicențiu D. Rădulescu, Zentralblatt MATH

在許多地方，對於一個定理提供了幾種不同的證明。這使得本書非常吸引人且易於閱讀。本書對於從事線性代數、算子理論、統計學、計算機科學、工程、應用數學、經濟學及其他學科的研究人員和研究生都非常有用。
-- Mohammad Sal Moslehian, Mathematical Reviews

作者簡介

Fuzhen Zhang is Distinguished Professor of Mathematics at Nova Southeastern University in Fort Lauderdale, Florida. He earned his Ph.D. in Mathematics from University of California at Santa Barbara (UCSB). Zhang is the author of Linear Algebra: Challenging Problems for Students (Johns Hopkins University Press) and Problems in Linear Algebra and Matrix Theory (World Scientific Publishing). In addition to this present textbook, he is also the editor of The Schur Complement and Its Applications (Springer). His academic work primarily focuses on topics in matrix analysis. Outside of academia, Zhang enjoys playing beach volleyball, pickleball, and singing Chinese folk songs.

作者簡介(中文翻譯)

張福珍是佛羅里達州勞德代爾堡的諾瓦東南大學數學特聘教授。他在加州大學聖巴巴拉分校（UCSB）獲得數學博士學位。張教授是《線性代數：學生挑戰問題》（約翰霍普金斯大學出版社）和《線性代數與矩陣理論中的問題》（世界科學出版社）的作者。除了這本教科書外，他還是《舒爾補數及其應用》（斯普林格）的編輯。他的學術工作主要集中在矩陣分析的主題上。在學術界之外，張教授喜歡打沙灘排球、打皮克球和唱中國民歌。

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