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9780534409159

Linear Algebra An Interactive Approach (with CD-ROM)

by ;
  • ISBN13:

    9780534409159

  • ISBN10:

    0534409156

  • Edition: CD
  • Format: Hardcover
  • Copyright: 2003-02-28
  • Publisher: Brooks Cole
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List Price: $354.95

Summary

Utilizing technology to enrich the learning experience, S.K. Jain and A.D. Gunawardena provide an exciting introduction to linear algebra. The accompanying CD-ROM contains the entire contents of the book in a searchable format. The CD-ROM also includes MATLAB drills, concept demonstrations, solutions, projects, and chapter tests. In addition to the CD-ROM, the Web site contains additional problems, projects, and applications, as well as support for MAPLE and Mathematica. In the book, the authors introduce matrices as a handy tool for solving systems of linear equations and then demonstrate that their utility goes far beyond this initial application. Students discover that hardly any area of modern mathematics exists where matrices do not have some application. Offering flexibility in the approach, this book can be used in a traditional course without technology or in a course using technology.

Table of Contents

Linear Systems and Matrices
1(32)
Linear Systems of Equations
1(4)
Elementary Operations and Gauss Elimination Method
5(6)
Homogeneous Linear Systems
11(5)
Introduction to Matrices and the Matrix of a Linear System
16(5)
Elementary Row Operations on a Matrix
21(7)
Proofs of Facts
28(1)
Chapter Review Questions and Project
29(4)
Algebra of Matrices
33(28)
Scalar Multiplication and Addition of Matrices
33(5)
Matrix Multiplication and Its Properties
38(11)
Transpose
49(3)
Proofs of Facts
52(3)
Chapter Review Questions and Projects
55(6)
Subspaces
61(30)
Linear Combination of Vectors
61(5)
Vector Subspaces
66(9)
Linear Dependence, Linear Independence, and Basis
75(9)
Proofs of Facts
84(3)
Chapter Review Questions and Project
87(4)
Rank
91(24)
Elementary Operations and Rank
91(6)
Null Space and Nullity of a Matrix
97(6)
Elementary Matrices
103(5)
Proofs of Facts
108(3)
Chapter Review Questions and Project
111(4)
Inverse, Rank Factorization, and LU-Decomposition
115(18)
Inverse of a Matrix and Its Properties
115(6)
Further Properties of Inverses
121(1)
Full-Rank Factorization
122(4)
LU-Decomposition of a Matrix
126(3)
Proofs of Facts
129(1)
Chapter Review Questions and Projects
130(3)
Determinants
133(18)
Determinant
133(6)
Properties of the Determinant
139(4)
Cofactors and Inverse of a Matrix
143(3)
Cramer's Rule
146(2)
Chapter Review Questions and Projects
148(3)
Eigenvalue Problems
151(36)
Eigenvalues and Eigenvectors
151(1)
Characteristic Polynomial
152(7)
Calculating Eigenvalues and Eigenvectors (Another Approach) and the Cayley-Hamilton Theorem
159(6)
Applications of the Cayley-Hamilton Theorem
165(8)
Properties of Eigenvalues, Diagonalizability, and Triangularizability
173(6)
Proofs of Facts
179(4)
Chapter Review Questions and Projects
183(4)
Inner Product Spaces
187(34)
Gram-Schmidt Orthogonalization Process
187(6)
Diagonalization of Symmetric Matrices
193(7)
Application of the Spectral Theorem
200(2)
Least-Squares Solution
202(7)
Generalized Inverse and Least-Squares Solution
209(3)
Proofs of Facts
212(3)
Chapter Review Questions and Projects
215(6)
Vector Spaces and Linear Mappings
221(26)
Vector Spaces
221(4)
Linear Dependence and Linear Independence
225(1)
Linear Mappings
226(7)
Some Properties of Linear Mappings: Image and Kernel
233(5)
Linear Mappings and Matrices
238(5)
Chapter Review Questions and Projects
243(4)
Determinants (Revisited)
247(22)
Permutations
247(4)
Determinants
251(6)
Cofactor Expansion
257(4)
Adjoint of a Matrix
261(2)
Cramer's Rule
263(1)
Product Theorem of Determinants
264(5)
Answers and Hints to Selected Exercises 269(30)
Drill Solutions Using Matlab 299(100)
Some Basic Matlab Operations 399(14)
Index 413

Supplemental Materials

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