Introduction to Linear Algebra,9780201658590

Introduction to Linear Algebra

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Edition: 5th
ISBN13: 9780201658590
ISBN10: 0201658593
Format: Hardcover
Pub. Date: 2001-07-26
Publisher(s): Pearson
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Summary

Introduction to Linear Algebra, 5/e is a foundation book that bridges both practical computation and theoretical principles. Due to its flexible table of contents, the book is accessible for both students majoring in the scientific, engineering, and social sciences, as well as students that want an introduction to mathematical abstraction and logical reasoning. In order to achieve the text's flexibility, the book centers on 3 principal topics: matrix theory and systems of linear equations, elementary vector space concepts, and the eigenvalue problem. This highly adaptable text can be used for a one-quarter or one-semester course at the sophomore/junior level, or for a more advanced class at the junior/senior level.

Table of Contents

Matrices and Systems of Linear Equations
1(112)
Introduction to Matrices and Systems of Linear Equations
2(12)
Echelon Form and Gauss--Jordan Elimination
14(14)
Consistent Systems of Linear Equations
28(11)
Applications (Optional)
39(7)
Matrix Operations
46(15)
Algebraic Properties of Matrix Operations
61(10)
Linear Independence and Nonsingular Matrices
71(9)
Data Fitting, Numerical Integration, and Numerical Differentiation (Optional)
80(12)
Matrix Inverses and Their Properties
92(21)
Vectors in 2-Space and 3-Space
113(50)
Vectors in the Plane
114(14)
Vectors in Space
128(7)
The Dot Product and the Cross Product
135(13)
Lines and Planes in Space
148(15)
The Vector Space Rn
163(112)
Introduction
164(3)
Vector Space Properties of Rn
167(9)
Examples of Subspaces
176(12)
Bases for Subspaces
188(14)
Dimension
202(12)
Orthogonal Bases for Subspaces
214(11)
Linear Transformations from Rn to Rm
225(18)
Least-Squares Solutions to Inconsistent Systems, with Applications to Data Fitting
243(12)
Theory and Practice of Least Squares
255(20)
The Eigenvalue Problem
275(82)
The Eigenvalue Problem for (2 × 2) Matrices
276(4)
Determinants and the Eigenvalue Problem
280(10)
Elementary Operations and Determinants (Optional)
290(8)
Eigenvalues and the Characteristic Polynomial
298(9)
Eigenvectors and Eigenspaces
307(8)
Complex Eigenvalues and Eigenvectors
315(10)
Similarity Transformations and Diagonalization
325(13)
Difference Equations; Markov Chains; Systems of Differential Equations (Optional)
338(19)
Vector Spaces and Linear Transformations
357(90)
Introduction
358(2)
Vector Spaces
360(8)
Subspaces
368(7)
Linear Independence, Bases, and Coordinates
375(13)
Dimension
388(4)
Inner-Product Spaces, Orthogonal Bases, and Projections (Optional)
392(11)
Linear Transformations
403(8)
Operations with Linear Transformations
411(8)
Matrix Representations for Linear Transformations
419(12)
Change of Basis and Diagonalization
431(16)
Determinants
447(36)
Introduction
448(1)
Cofactor Expansions of Determinants
448(7)
Elementary Operations and Determinants
455(10)
Cramer's Rule
465(6)
Applications of Determinants: Inverses and Wronksians
471(12)
Eigenvalues and Applications
483
Quadratic Forms
484
Systems of Differential Equations
493
Transformation to Hessenberg Form
502
Eigenvalues of Hessenberg Matrices
510
Householder Transformations
519
The QR Factorization and Least-Squares Solutions
531
Matrix Polynomials and the Cayley--Hamilton Theorem
540
Generalized Eigenvectors and Solutions of Systems of Differential Equations
546
Appendix: An Introduction to MATLAB AP1
Answers to Selected Odd-Numbered Exercises AN1
Index I1

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