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Elementary Linear Algebra 11th Revised edition [Hardback]

3.84/5 (24 ratings by Goodreads)
  • Formāts: Hardback, 592 pages, height x width x depth: 257x221x25 mm, weight: 1171 g
  • Izdošanas datums: 04-Nov-2013
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 1118473507
  • ISBN-13: 9781118473504
Citas grāmatas par šo tēmu:
  • Formāts: Hardback, 592 pages, height x width x depth: 257x221x25 mm, weight: 1171 g
  • Izdošanas datums: 04-Nov-2013
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 1118473507
  • ISBN-13: 9781118473504
Citas grāmatas par šo tēmu:
Anton presents this linear algebra textbook for introductory undergraduate courses, organized so as to enable skipping over portions that require calculus background. The text begins with linear equations, matrices, and determinants, then moves onto Euclidean vector spaces, Rn, and general vector spaces. Eigenvalues and eigenvectors, inner product spaces, diagonalization and quadratic forms take up the middle of the book. Finally general linear transformations are treated, and numerical methods are discussed in the last chapter. This edition is updated to introduce linear transformations earlier, in a section at the end of the matrix chapter, and contains new exercises, an expanded appendix on proofs, and some reorganization and rewriting for flow. Annotation ©2014 Book News, Inc., Portland, OR (booknews.com)

Anton's Elementary Linear Algebra continues to provide a strong recourse for readers due to his sound mathematics and clear exposition. This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation.

Chapter 1 Systems of Linear Equations and Matrices
1(104)
1.1 Introduction to Systems of Linear Equations
2(9)
1.2 Gaussian Elimination
11(14)
1.3 Matrices and Matrix Operations
25(14)
1.4 Inverses; Algebraic Properties of Matrices
39(13)
1.5 Elementary Matrices and a Method for Finding A-1
52(9)
1.6 More on Linear Systems and Invertible Matrices
61(6)
1.7 Diagonal, Triangular, and Symmetric Matrices
67(8)
1.8 Matrix Transformations
75(9)
1.9 Applications of Linear Systems
84(12)
Network Analysis (Traffic Flow)
84(2)
Electrical Circuits
86(2)
Balancing Chemical Equations
88(3)
Polynomial Interpolation
91(5)
1.10 Application: Leontief Input-Output Models
96(9)
Chapter 2 Determinants
105(26)
2.1 Determinants by Cofactor Expansion
105(8)
2.2 Evaluating Determinants by Row Reduction
113(5)
2.3 Properties of Determinants; Cramer's Rule
118(13)
Chapter 3 Euclidean Vector Spaces
131(52)
3.1 Vectors in 2-Space, 3-Space, and n-Space
131(11)
3.2 Norm, Dot Product, and Distance in Rn
142(13)
3.3 Orthogonality
155(9)
3.4 The Geometry of Linear Systems
164(8)
3.5 Cross Product
172(11)
Chapter 4 General Vector Spaces
183(108)
4.1 Real Vector Spaces
183(8)
4.2 Subspaces
191(11)
4.3 Linear Independence
202(10)
4.4 Coordinates and Basis
212(9)
4.5 Dimension
221(8)
4.6 Change of Basis
229(8)
4.7 Row Space, Column Space, and Null Space
237(11)
4.8 Rank, Nullity, and the Fundamental Matrix Spaces
248(11)
4.9 Basic Matrix Transformations in R2 and R3
259(11)
4.10 Properties of Matrix Transformations
270(10)
4.11 Application: Geometry of Matrix Operators on R2
280(11)
Chapter 5 Eigenvalues and Eigenvectors
291(54)
5.1 Eigenvalues and Eigenvectors
291(11)
5.2 Diagonalization
302(11)
5.3 Complex Vector Spaces
313(13)
5.4 Application: Differential Equations
326(6)
5.5 Application: Dynamical Systems and Markov Chains
332(13)
Chapter 6 Inner Product Spaces
345(56)
6.1 Inner Products
345(10)
6.2 Angle and Orthogonality in Inner Product Spaces
355(9)
6.3 Gram--Schmidt Process; QR-Decomposition
364(14)
6.4 Best Approximation; Least Squares
378(9)
6.5 Application: Mathematical Modeling Using Least Squares
387(7)
6.6 Application: Function Approximation; Fourier Series
394(7)
Chapter 7 Diagonalization and Quadratic Forms
401(46)
7.1 Orthogonal Matrices
401(8)
7.2 Orthogonal Diagonalization
409(8)
7.3 Quadratic Forms
417(12)
7.4 Optimization Using Quadratic Forms
429(8)
7.5 Hermitian, Unitary, and Normal Matrices
437(10)
Chapter 8 General Linear Transformations
447(44)
8.1 General Linear Transformations
447(11)
8.2 Compositions and Inverse Transformations
458(8)
8.3 Isomorphism
466(6)
8.4 Matrices for General Linear Transformations
472(9)
8.5 Similarity
481(10)
Chapter 9 Numerical Methods
491
9.1 LU-Decompositions
491(10)
9.2 The Power Method
501(8)
9.3 Comparison of Procedures for Solving Linear Systems
509(5)
9.4 Singular Value Decomposition
514(7)
9.5 Application: Data Compression Using Singular Value Decomposition
521
Appendix A Working with Proofs 1(4)
Appendix B Complex Numbers 5(8)
Answers to Exercises 13
Index 1