-
出版商:
Springer
-
出版日期:
2025-08-31
-
售價:
$2,400
-
貴賓價:
9.5 折
$2,280
-
語言:
英文
-
頁數:
389
-
裝訂:
Quality Paper - also called trade paper
-
ISBN:
3031932595
-
ISBN-13:
9783031932595
-
相關分類:
線性代數 Linear-algebra
商品描述
This self-contained textbook, now in a thoroughly revised and expanded second edition, takes a matrix-oriented approach to Linear Algebra. It presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its derivation. Throughout, the book emphasizes the practical applicability of results. It therefore also covers special topics in Applied Linear Algebra, such as matrix functions, the singular value decomposition, the Kronecker product, and linear matrix equations. New to this edition are topics such as the Frobenius canonical form and a more detailed treatment of infinite-dimensional vector spaces, along with many additional exercises. The book's matrix-oriented approach enhances intuition and simplifies abstract concepts, making them easier to understand and to apply in real-world scenarios. Key applications are illustrated through detailed examples. Additionally, several "MATLAB Minutes" allow students to explore concepts and results through computational experiments, supported by a brief introduction to MATLAB fundamentals. Together with over 380 exercises, this encourages active engagement with the material.
商品描述(中文翻譯)
這本獨立的教科書，現在已經全面修訂並擴充至第二版，採取以矩陣為導向的線性代數方法。它呈現了完整的理論，包括所有細節和證明，最終導出喬丹標準型（Jordan canonical form）。全書強調結果的實用性，因此也涵蓋了應用線性代數中的特殊主題，如矩陣函數、奇異值分解（singular value decomposition）、克羅內克積（Kronecker product）和線性矩陣方程。這一版新增的主題包括弗羅貝尼烏斯標準型（Frobenius canonical form）以及對無限維向量空間的更詳細處理，並增加了許多額外的練習題。
本書的矩陣導向方法增強了直覺，簡化了抽象概念，使其更易於理解和應用於現實場景。關鍵應用通過詳細的例子進行說明。此外，幾個「MATLAB 分鐘」讓學生通過計算實驗探索概念和結果，並附有簡要的 MATLAB 基礎介紹。結合380多道練習題，這鼓勵學生積極參與學習材料。
作者簡介
Jörg Liesen's research interests are in Numerical Linear Algebra, Matrix Theory, Constructive Approximation, and Computational Complex Analysis. A particular focus of his work is the convergence and stability analysis of iterative methods for solving large linear algebraic problems, which occur throughout science and engineering applications. He is also interested in the history of Mathematics, and in particular of Linear Algebra. He is the recipient of several prizes and awards for his mathematical work, including the Householder Award, the Emmy Noether Fellowship and the Heisenberg Professorship of the DFG. He likes to teach and pursue Mathematics as a lively subject, connecting theory with an ever-increasing variety of fascinating applications. Volker Mehrmann's research interests are in Numerical Mathematics, Control Theory, Matrix Theory, Mathematical Modeling as well as Scientific Computing. In recent years he has focused on the development and analysis of numerical methods for nonlinear eigenvalue problems and differential-algebraic systems of port-Hamiltonian structure with applications in many fields such as mechanical systems, electronic circuit simulation and acoustic field computations. He is co-editor-in-chief of the journal Linear Algebra and its Applications and editor of many other journals in Linear Algebra and Numerical Analysis. He believes that Mathematics has become a central ingredient for the societal development of the 21st century and that mathematical methods play the key role in the modeling, simulation, control and optimization of all areas of technological development.
作者簡介(中文翻譯)
約爾格·利森（Jörg Liesen）的研究興趣包括數值線性代數、矩陣理論、構造近似以及計算複雜分析。他的工作特別關注於解決大型線性代數問題的迭代方法的收斂性和穩定性分析，這些問題在科學和工程應用中隨處可見。他也對數學的歷史感興趣，特別是線性代數的歷史。他因其數學工作獲得了多個獎項，包括豪斯霍爾德獎（Householder Award）、艾米·諾特獎學金（Emmy Noether Fellowship）以及德國研究基金會的海森堡教授職位（Heisenberg Professorship）。他喜歡教學，並將數學視為一個充滿活力的學科，將理論與日益多樣化的迷人應用相連結。
福爾克·梅爾曼（Volker Mehrmann）的研究興趣包括數值數學、控制理論、矩陣理論、數學建模以及科學計算。近年來，他專注於非線性特徵值問題和具有端口哈密頓結構的微分代數系統的數值方法的開發和分析，這些方法在機械系統、電子電路模擬和聲場計算等多個領域中都有應用。他是期刊《線性代數及其應用》（Linear Algebra and its Applications）的共同主編，並擔任多本線性代數和數值分析期刊的編輯。他認為數學已成為21世紀社會發展的核心要素，數學方法在所有技術發展領域的建模、模擬、控制和優化中扮演著關鍵角色。
