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

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.

第一版的好評如潮：

「. . . 推薦給老師、研究人員以及研究生。事實上，[這本書] 應該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和實踐，特別關注其分析方面以及該主題的眾多應用。除了全面涵蓋線性方程、矩陣、向量空間、博弈論和數值分析等內容外，第二版還增加了一些便於學生理解的內容，包括在前幾章擴展了主題的涵蓋範圍、增加了額外的練習題以及選定問題的解答。

開頭的章節專注於有限維向量空間的抽象結構，隨後的章節討論了凸性和對偶定理，並描述了規範線性空間和規範空間之間的線性映射的基礎知識。

為了反映該主題的最新內容，我們還進行了進一步的更新和修訂，包括：

- QR算法用於找到自伴矩陣的特徵值
- Householder算法將自伴矩陣轉換為三對角形式
- 單位球的緊致性作為規範線性空間有限維度的標準

此外，我們還新增了八個附錄，涵蓋了以下主題：快速傅立葉變換、譜半徑定理、洛倫茲群、有限維度的緊致性標準、評論家的特徵、Liapunov穩定性標準的證明、矩陣的約當喬登形式的構造，以及Carl Pearcy對Halmos關於矩陣數值範圍的猜想的優雅證明。

《線性代數及其應用》第二版清晰、簡潔、組織良好，是高年級本科生和研究生線性代數課程的優秀教材。其全面的內容也使其成為業界專業人士的理想參考書或自學材料。