Advanced Linear and Matrix Algebra

Johnston, Nathaniel

  • 出版商: Springer
  • 出版日期: 2021-05-20
  • 售價: $2,480
  • 貴賓價: 9.5$2,356
  • 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
  • 立即出貨(限量) (庫存=1)

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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和幾何之間的互動,以激發對高級線性代數技巧的研究興趣。矩陣和線性變換被呈現為同一個硬幣的兩面,它們之間的聯繫激發了整本書的探究。在線性代數的第一門課程的基礎上,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。概念通過具體的例子進行解釋,提供了通往高級技巧的易於理解的途徑。

從包括坐標、同構、正交性和投影的向量空間的研究開始,本書接著專注於矩陣分解。探討了許多分解,包括Shur、譜、奇異值和Jordan分解。在每種情況下,作者將新技術與熟悉的技術聯繫起來,形成一套有條理的工具。張量和多線性完成了本書,包括對Kronecker乘積、多線性變換和張量乘積的研究。整本書都有「額外主題」部分,以廣泛的想法和應用來補充核心內容,從QR和Cholesky分解到矩陣值線性映射和半定規劃。每個部分都附有各種難度的練習題。

《高級線性和矩陣代數》為數學、數據分析等學科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緣註解展示了作者的視覺方法。假設已經修習過基於證明的線性代數的第一門課程。作者的配套著作《線性和矩陣代數入門》是理想的準備材料。

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 是加拿大新布倫瑞克省 Mount Allison 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紛亂理論相關的問題。他的合著作品《線性和矩陣代數入門》也由 Springer 出版。