Linear Algebra and Its Applications, 2/e (美國原版)
暫譯: 線性代數及其應用（第二版）

Peter D. Lax

Linear Algebra and Its Applications, 2/e (美國原版)

買這商品的人也買了...

相關主題

商品描述

Praise for the First Edition

". . .recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematician's bookshelf." -American Mathematical Monthly

Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book's accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems.

Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces.

Further updates and revisions have been included to reflect the most up-to-date coverage of the topic, including:

  • The QR algorithm for finding the eigenvalues of a self-adjoint matrix
  • The Householder algorithm for turning self-adjoint matrices into tridiagonal form
  • The compactness of the unit ball as a criterion of finite dimensionality of a normed linear space

Additionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov's stability criterion; the construction of the Jordan Canonical form of matrices; and Carl Pearcy's elegant proof of Halmos' conjecture about the numerical range of matrices.

Clear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate- and graduate-level courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or self-study for industry professionals.

商品描述(中文翻譯)

對於第一版的讚譽

「……推薦給教師和研究人員以及研究生。事實上，[它] 在每位數學家的書架上都有一席之地。」-《美國數學月刊》

《線性代數及其應用（第二版）》將線性代數呈現為線性空間和線性映射的理論與實踐，獨特地專注於分析方面以及該主題的眾多應用。除了對線性方程、矩陣、向量空間、博弈論和數值分析的全面覆蓋外，第二版還增加了對學生友好的內容，提升了本書的可讀性，包括早期章節的主題擴展、額外的練習題和選定問題的解答。

前幾章專注於有限維向量空間的抽象結構，隨後的章節則討論凸性和對偶定理，並描述了範數線性空間的基本概念以及範數空間之間的線性映射。

此外，還包含了進一步的更新和修訂，以反映該主題的最新內容，包括：

- 用於尋找自伴隨矩陣特徵值的 QR 演算法
- 將自伴隨矩陣轉換為三對角形式的 Householder 演算法
- 單位球的緊性作為範數線性空間有限維度的標準

此外，還新增了八個附錄，涵蓋以下主題：快速傅立葉變換；譜半徑定理；洛倫茲群；有限維度的緊性標準；評論者的特徵；李亞普諾夫穩定性標準的證明；矩陣的喬丹標準形構造；以及卡爾·皮爾西對哈爾莫斯有關矩陣數值範圍猜想的優雅證明。

《線性代數及其應用（第二版）》清晰、簡潔且組織優秀，是高級本科和研究生線性代數課程的絕佳教材。其對該主題的全面處理也使其成為行業專業人士理想的參考書或自學資料。

類似商品