Linear Algebra / by Jin Ho Kwak, Sungpyo Hong
| データ種別 | 電子ブック |
|---|---|
| 版 | Second Edition |
| 出版者 | Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser |
| 出版年 | 2004 |
| 本文言語 | 英語 |
| 大きさ | XV, 390 p. 9 illus : online resource |
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| 内容注記 | 1 Linear Equations and Matrices 1.1 Systems of linear equations 1.2 Gaussian elimination 1.3 Sums and scalar multiplications of matrices 1.4 Products of matrices 1.5 Block matrices 1.6 Inverse matrices 1.7 Elementary matrices and finding A?1 1.8 LDU factorization 1.9 Applications 1.10 Exercises 2 Determinants 2.1 Basic properties of the determinant 2.2 Existence and uniqueness of the determinant 2.3 Cofactor expansion 2.4 Cramer’s rule 2.5 Applications 2.6 Exercises 3 Vector Spaces 3.1 The n-space ?n and vector spaces 3.2 Subspaces 3.3 Bases 3.4 Dimensions 3.5 Row and column spaces 3.6 Rank and nullity 3.7 Bases for subspaces 3.8 Invertibility 3.9 Applications 3.10 Exercises> 4 Linear Transformations 4.1 Basic propertiesof linear transformations 4.2 Invertiblelinear transformations 4.3 Matrices of linear transformations 4.4 Vector spaces of linear transformations 4.5 Change of bases 4.6 Similarity 4.7. Applications 4.8 Exercises 5 Inner Product Spaces 5.1 Dot products and inner products 5.2 The lengths and angles of vectors 5.3 Matrix representations of inner products 5.4 Gram-Schmidt orthogonalization 5.5 Projections 5.6 Orthogonal projections 5.7 Relations of fundamental subspaces 5.8 Orthogonal matrices and isometries 5.9 Applications 5.10 Exercises 6 Diagonalization 6.1 Eigenvalues and eigenvectors 6.2 Diagonalization of matrices 6.3 Applications 6.4 Exponential matrices 6.5 Applications continued 6.6 Diagonalization of linear transformations 6.7 Exercises 7 Complex Vector Spaces 7.1 The n-space ?n and complex vector spaces 7.2 Hermitian and unitary matrices 7.3 Unitarily diagonalizable matrices 7.4 Normal matrices 7.5 Application 7.6 Exercises 8 Jordan Canonical Forms 8.1 Basic properties of Jordan canonical forms 8.2 Generalized eigenvectors 8.3 The power Ak and the exponential eA 8.4 Cayley-Hamilton theorem 8.5 The minimal polynomial of a matrix> 8.6 Applications 8.7 Exercises 9 Quadratic Forms 9.1 Basic properties of quadratic forms 9.2 Diagonalization of quadratic forms 9.3 A classification of level surfaces 9.4 Characterizations of definite forms 9.5 Congruence relation 9.6 Bilinear and Hermitian forms 9.7 Diagonalization of bilinear or Hermitian forms 9.8 Applications 9.9 Exercises Selected Answers and Hints |
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| 一般注記 | "A logical development of the subject…all the important theorems and results are discussed in terms of simple worked examples. The student's understanding…is tested by problems at the end of each subsection, and every chapter ends with exercises." --- "Current Science" (Review of the First Edition) A cornerstone of undergraduate mathematics, science, and engineering, this clear and rigorous presentation of the fundamentals of linear algebra is unique in its emphasis and integration of computational skills and mathematical abstractions. The power and utility of this beautiful subject is demonstrated, in particular, in its focus on linear recurrence, difference and differential equations that affect applications in physics, computer science, and economics. Key topics and features include: * Linear equations, matrices, determinants, vector spaces, complex vector spaces, inner products, Jordan canonical forms, and quadratic forms * Rich selection of examples and explanations, as well as a wide range of exercises at the end of every section * Selected answers and hints This second edition includes substantial revisions, new material on minimal polynomials and diagonalization, as well as a variety of new applications. The text will serve theoretical and applied courses and is ideal for self-study. With its important approach to linear algebra as a coherent part of mathematics and as a vital component of the natural and social sciences, "Linear Algebra, Second Edition" will challenge and benefit a broad audience |
| 著者標目 | *Kwak, Jin Ho author Hong, Sungpyo author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Computer science -- Mathematics 全ての件名で検索 LCSH:Algebra LCSH:Matrix theory LCSH:Applied mathematics LCSH:Engineering mathematics LCSH:Economic theory FREE:Mathematics FREE:Algebra FREE:Linear and Multilinear Algebras, Matrix Theory FREE:Mathematics of Computing FREE:Math Applications in Computer Science FREE:Appl.Mathematics/Computational Methods of Engineering FREE:Economic Theory/Quantitative Economics/Mathematical Methods |
| 分 類 | DC23:512 |
| 巻冊次 | ISBN:9780817681944 
|
| ISBN | 9780817681944 |
| URL | http://dx.doi.org/10.1007/978-0-8176-8194-4 |
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