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Linear Algebra An Interactive Approach

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ISBN-10: 0534409156

ISBN-13: 9780534409159

Edition: 2004

Authors: Surender K. Jain, Ananda D. Gunawardena

List price: $335.95
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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…    
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Book details

List price: $335.95
Copyright year: 2004
Publisher: Brooks/Cole
Publication date: 2/28/2003
Binding: Hardcover
Pages: 432
Size: 8.00" wide x 9.75" long x 0.75" tall
Weight: 1.870
Language: English

Linear Systems and Matrices
Linear Systems of Equations
Elementary Operations and Gauss Elimination Method
Homogeneous Linear Systems
Introduction to Matrices and the Matrix of a Linear System
Elementary Row Operations on a Matrix
Proofs of Facts
Chapter Review Questions and Project
Algebra of Matrices
Scalar Multiplication and Addition of Matrices
Matrix Multiplication and Its Properties
Transpose
Proofs of Facts
Chapter Review Questions and Projects
Subspaces
Linear Combination of Vectors
Vector Subspaces
Linear Dependence, Linear Independence, and Basis
Proofs of Facts
Chapter Review Questions and Project
Rank
Elementary Operations and Rank
Null Space and Nullity of a Matrix
Elementary Matrices
Proofs of Facts
Chapter Review Questions and Project
Inverse, Rank Factorization, and LU-Decomposition
Inverse of a Matrix and Its Properties
Further Properties of Inverses
Full-Rank Factorization
LU-Decomposition of a Matrix
Proofs of Facts
Chapter Review Questions and Projects
Determinants
Determinant
Properties of the Determinant
Cofactors and Inverse of a Matrix
Cramer's Rule
Chapter Review Questions and Projects
Eigenvalue Problems
Eigenvalues and Eigenvectors
Characteristic Polynomial
Calculating Eigenvalues and Eigenvectors (Another Approach) and the Cayley-Hamilton Theorem
Applications of the Cayley-Hamilton Theorem
Properties of Eigenvalues, Diagonalizability, and Triangularizability
Proofs of Facts
Chapter Review Questions and Projects
Inner Product Spaces
Gram-Schmidt Orthogonalization Process
Diagonalization of Symmetric Matrices
Application of the Spectral Theorem
Least-Squares Solution
Generalized Inverse and Least-Squares Solution
Proofs of Facts
Chapter Review Questions and Projects
Vector Spaces and Linear Mappings
Vector Spaces
Linear Dependence and Linear Independence
Linear Mappings
Some Properties of Linear Mappings: Image and Kernel
Linear Mappings and Matrices
Chapter Review Questions and Projects
Determinants (Revisited)
Permutations
Determinants
Cofactor Expansion
Adjoint of a Matrix
Cramer's Rule
Product Theorem of Determinants
Answers and Hints to Selected Exercises
Drill Solutions Using Matlab
Some Basic Matlab Operations
Index