Matrix Mathematics: Theory, Facts, and Formulas, 2/e (Paperback)

Dennis S. Bernstein

  • 出版商: Princeton University
  • 出版日期: 2009-07-26
  • 售價: $4,040
  • 貴賓價: 9.5$3,838
  • 語言: 英文
  • 頁數: 1184
  • 裝訂: Paperback
  • ISBN: 0691140391
  • ISBN-13: 9780691140391
  • 相關分類: 線性代數 Linear-algebra
  • 已絕版

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商品描述

When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices.

Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminating remarks. Beginning with preliminaries on sets, functions, and relations,Matrix Mathematics covers all of the major topics in matrix theory, including matrix transformations; polynomial matrices; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; vector and matrix norms; the matrix exponential and stability theory; and linear systems and control theory. Also included are a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. This significantly expanded edition of Matrix Mathematics features a wealth of new material on graphs, scalar identities and inequalities, alternative partial orderings, matrix pencils, finite groups, zeros of multivariable transfer functions, roots of polynomials, convex functions, and matrix norms.

  • Covers hundreds of important and useful results on matrix theory, many never before available in any book
  • Provides a list of symbols and a summary of conventions for easy use
  • Includes an extensive collection of scalar identities and inequalities
  • Features a detailed bibliography and author index with page references
  • Includes an exhaustive subject index with cross-referencing

商品描述(中文翻譯)

當《Matrix Mathematics》於2005年首次出版時,迅速成為工程、科學和應用數學各個領域中使用矩陣的使用者必備的參考書。在這本完全更新和擴充的新版中,作者匯集了最新的矩陣理論成果,使這本書成為最完整、最新和最易於使用的矩陣書籍。

每一章節都描述了相關的背景理論,然後是專門的結果。數百個恆等式、不等式和矩陣事實都清晰而嚴謹地陳述,並附有交叉引用、文獻引用和啟發性的評論。從集合、函數和關係的基礎開始,《Matrix Mathematics》涵蓋了矩陣理論的所有主要主題,包括矩陣變換、多項式矩陣、矩陣分解、廣義逆、Kronecker和Schur代數、半正定矩陣、向量和矩陣範數、矩陣指數和穩定性理論,以及線性系統和控制理論。還包括詳細的符號列表、符號和慣例摘要、廣泛的文獻目錄和作者索引(附有頁碼參考)以及詳盡的主題索引。這本大幅擴充的《Matrix Mathematics》新版增加了大量關於圖形、標量恆等式和不等式、替代偏序、矩陣鉛筆、有限群、多變量傳輸函數的零點、多項式的根、凸函數和矩陣範數的新材料。

- 包含數百個重要且有用的矩陣理論結果,其中許多在任何書籍中都是首次出現
- 提供符號列表和慣例摘要,方便使用
- 包括大量的標量恆等式和不等式
- 具有詳細的文獻目錄和作者索引(附有頁碼參考)
- 包括詳盡的主題索引,具有交叉引用功能