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$ 355 | 若爾當典範形：理論與實踐(英文)
作者：（美）史蒂文·H.溫特勞布 出版社：哈爾濱工業大學出版社 出版日期：2021-07-01 語言：簡體中文 規格：平裝 / 153頁 / 19 x 26 x 1 cm / 普通級/ 1-1  博客來 - 數學
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圖書名稱：若爾當典範形：理論與實踐(英文)
內容簡介
本書共分三章，主要介紹了若爾當典範形的相關內容，內容包括線性變換或矩陣的JCF，編碼有關該線性變換或矩陣的所有結構資訊。本書概括了JCF的發展歷程，從JCF的背景入手，主要介紹了若爾當典範形及其相關概念、特徵值、廣義特徵向量、特徵多項式和最小多項式，討論了對角化問題，證明了漢米爾頓—凱萊定理。本書還引入了矩陣的特徵結構圖、一種使JCF清晰的圖形標記法。本書適合高等院校師生、研究生及相關愛好者參考閱讀。
目錄
Preface
1 Fundamentals on Vector Spaces and Linear Transformations
1.1 Bases and Coordinates
1.2 Linear Transformations and Matrices
1.3 Some Special Matrices
1.4 Polynomials in T and A
1.5 Subspaces,Complements,and Invariant Subspaces
2 The Structure of a Linear Transformation
2.1 Eigenvalues,Eigenvectors,and Generalized Eigenvectors
2.2 The Minimum Polynomial
2.3 Reduction to BDBUTCD Form
2.4 The Diagonalizable Case
2.5 Reduction to Jordan Canonical Form
2.6 Exercises
3 An Algorithm for Jordan Canonical Form and Jordan Basis
3.1 The ESP of a Linear Transformation
3.2 The Algorithm for Jordan Canonical Form
3.3 The Algorithm for a Jordan Basis
3.4 Examples
3.5 Exercises
A Answers to odd-numbered exercises
A.1 Answers to Exercises-Chapter 2
A.2 Answers to Exercises-Chapter 3
Notation
Index
編輯手記
1 Fundamentals on Vector Spaces and Linear Transformations
1.1 Bases and Coordinates
1.2 Linear Transformations and Matrices
1.3 Some Special Matrices
1.4 Polynomials in T and A
1.5 Subspaces,Complements,and Invariant Subspaces
2 The Structure of a Linear Transformation
2.1 Eigenvalues,Eigenvectors,and Generalized Eigenvectors
2.2 The Minimum Polynomial
2.3 Reduction to BDBUTCD Form
2.4 The Diagonalizable Case
2.5 Reduction to Jordan Canonical Form
2.6 Exercises
3 An Algorithm for Jordan Canonical Form and Jordan Basis
3.1 The ESP of a Linear Transformation
3.2 The Algorithm for Jordan Canonical Form
3.3 The Algorithm for a Jordan Basis
3.4 Examples
3.5 Exercises
A Answers to odd-numbered exercises
A.1 Answers to Exercises-Chapter 2
A.2 Answers to Exercises-Chapter 3
Notation
Index
編輯手記
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