Advanced Linear and Matrix Algebra
暫譯: 高級線性與矩陣代數

Johnston, Nathaniel

  • 出版商: Springer
  • 出版日期: 2021-05-20
  • 售價: $2,470
  • 貴賓價: 9.5$2,347
  • 語言: 英文
  • 頁數: 497
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3030528146
  • ISBN-13: 9783030528140
  • 相關分類: 線性代數 Linear-algebra
  • 海外代購書籍(需單獨結帳)

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商品描述

This textbook emphasizes the interplay between algebra and geometry to motivate the study of advanced linear algebra techniques. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. Building on a first course in linear algebra, this book offers readers a deeper understanding of abstract structures, matrix decompositions, multilinearity, and tensors. Concepts draw on concrete examples throughout, offering accessible pathways to advanced techniques.

Beginning with a study of vector spaces that includes coordinates, isomorphisms, orthogonality, and projections, the book goes on to focus on matrix decompositions. Numerous decompositions are explored, including the Shur, spectral, singular value, and Jordan decompositions. In each case, the author ties the new technique back to familiar ones, to create a coherent set of tools. Tensors and multilinearity complete the book, with a study of the Kronecker product, multilinear transformations, and tensor products. Throughout, "Extra Topic" sections augment the core content with a wide range of ideas and applications, from the QR and Cholesky decompositions, to matrix-valued linear maps and semidefinite programming. Exercises of all levels accompany each section.

Advanced Linear and Matrix Algebra offers students of mathematics, data analysis, and beyond the essential tools and concepts needed for further study. The engaging color presentation and frequent marginal notes showcase the author's visual approach. A first course in proof-based linear algebra is assumed. An ideal preparation can be found in the author's companion volume, Introduction to Linear and Matrix Algebra.

商品描述(中文翻譯)

這本教科書強調代數與幾何之間的相互作用,以激發對進階線性代數技術的學習動機。矩陣和線性變換被視為同一事物的兩面,其連結激發了全書的探究。基於線性代數的初階課程,本書為讀者提供了對抽象結構、矩陣分解、多線性和張量的更深入理解。全書通過具體的例子來引入概念,提供通往進階技術的可及途徑。

本書從研究向量空間開始,涵蓋坐標、同構、正交性和投影,接著專注於矩陣分解。探討了多種分解,包括 Shur 分解、譜分解、奇異值分解和 Jordan 分解。在每一種情況下,作者將新技術與熟悉的技術聯繫起來,以創建一套連貫的工具。張量和多線性構成了本書的結尾,研究了 Kronecker 乘積、多線性變換和張量乘積。在整個過程中,「額外主題」部分增補了核心內容,涵蓋了從 QR 和 Cholesky 分解到矩陣值線性映射和半正定規劃的廣泛想法和應用。每個部分都附有各級別的練習題。

《進階線性與矩陣代數》為數學、數據分析及其他領域的學生提供了進一步學習所需的基本工具和概念。引人入勝的彩色呈現和頻繁的邊註展示了作者的視覺化方法。假設讀者已完成基於證明的線性代數初階課程。理想的準備可以在作者的伴隨書籍《線性與矩陣代數導論》中找到。

作者簡介

Nathaniel Johnston is an Associate Professor of Mathematics at Mount Allison University in New Brunswick, Canada. His research makes use of linear algebra, matrix analysis, and convex optimization to tackle questions related to the theory of quantum entanglement. His companion volume, Introduction to Linear and Matrix Algebra, is also published by Springer.

作者簡介(中文翻譯)

Nathaniel Johnston 是加拿大新不倫瑞克省蒙特艾利森大學的數學副教授。他的研究利用線性代數、矩陣分析和凸優化來解決與量子糾纏理論相關的問題。他的伴隨著作《線性與矩陣代數導論》也由施普林格出版。