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Linear Algebra Ideas and Applications

ISBN-10: 0470178841
ISBN-13: 9780470178843
Edition: 3rd 2008
List price: $149.00 Buy it from $2.99
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Description: Linear Algebra: Ideas and Applications, Third Edition has been updated and revised, but its parallel structure (abstract concepts are introduced along with computational) and concepts remain intact. The book covers a number of applications of linear  More...

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Book details

List price: $149.00
Edition: 3rd
Copyright year: 2008
Publisher: John Wiley & Sons, Incorporated
Publication date: 7/21/2008
Binding: Hardcover
Pages: 504
Size: 6.50" wide x 9.25" long x 1.00" tall
Weight: 2.068
Language: English

Linear Algebra: Ideas and Applications, Third Edition has been updated and revised, but its parallel structure (abstract concepts are introduced along with computational) and concepts remain intact. The book covers a number of applications of linear algebra and features a unique treatment of vector spaces, proofs, and computations. The text explores linear algebra using an approach that introduces abstract concepts as they are needed to fully understand the computations.

Systems of Linear Equations
The Vector Space of m x n Matrices
The Space R[superscript n]
Linear Combinations and Linear Dependence
What Is a Vector Space?
Why Prove Anything?
True-False Questions
Exercises
Computer Projects
Exercises
Applications to Graph Theory I
Self-Study Questions
Exercises
Systems
Rank: The Maximum Number of Linearly Independent Equations
True-False Questions
Exercises
Computer Projects
Exercises
Applications to Circuit Theory
Self-Study Questions
Exercises
Gaussian Elimination
Spanning in Polynomial Spaces
Computational Issues: Pivoting
True-False Questions
Exercises
Computational Issues: Flops
Computer Projects
Exercises
Applications to Traffic Flow
Self-Study Questions
Exercises
Column Space and Nullspace
Subspaces
Subspaces of Functions
True-False Questions
Exercises
Computer Projects
Exercises
Applications to Predator-Prey Problems
Self-Study Questions
Exercises
Chapter Summary
Linear Independence and Dimension
The Test for Linear Independence
Bases for the Column Space
Testing Functions for Independence
True-False Questions
Exercises
Computer Projects
Exercises
Dimension
True-False Questions
Exercises
Computer Projects
Exercises
Applications to Calculus
Self-Study Questions
Exercises
Applications to Differential Equations
Self-Study Questions
Exercises
Applications to the Harmonic Oscillator
Self-Study Questions
Exercises
Computer Projects
Exercises
Row Space and the rank-nullity theorem
Bases for the Row Space
Rank-Nullity Theorem
Computational Issues: Computing Rank
True-False Questions
Exercises
Computer Projects
Exercises
Chapter Summary
Linear Transformations
The Linearity Properties
True-False Questions
Exercises
Computer Projects
Exercises
Applications to Control Theory
Self-Study Questions
Exercises
Matrix Multiplication (Composition)
Partitioned Matrices
Computational Issues: Parallel Computing
True-False Questions
Exercises
Computer Projects
Exercises
Applications to Graph Theory II
Self-Study Questions
Exercises
Inverses
Computational Issues: Reduction versus Inverses
True-False Questions
Exercises
Computer Projects
Ill-Conditioned Systems
Exercises
Applications to Economics
Self-Study Questions
Exercises
The LU Factorization
Exercises
Computer Projects
Exercises
The Matrix of a Linear Transformation
Coordinates
Application to Differential Equations
Isomorphism
Invertible Linear Transformations
True-False Questions
Exercises
Computer Projects
Exercises
Chapter Summary
Determinants
Definition of the Determinant
The Rest of the Proofs
True-False Questions
Exercises
Computer Projects
Reduction and Determinants
Uniqueness of the Determinant
True-False Questions
Exercises
Application to Volume
Self-Study Questions
Exercises
A Formula for Inverses
Cramer's Rule
True-False Questions
Exercises
Chapter Summary
Eigenvectors and Eigenvalues
Eigenvectors
True-False Questions
Exercises
Computer Projects
Exercises
Application to Markov Processes
Exercises
Diagonalization
Powers of Matrices
True-False Questions
Exercises
Computer Projects
Exercises
Application to Systems of Differential Equations
Self-Study Questions
Exercises
Complex Eigenvectors
Complex Vector Spaces
Exercises
Computer Projects
Exercises
Chapter Summary
Orthogonality
The Scalar Product in R[superscript n]
Orthogonal/Orthonormal Bases and Coordinates
True-False Questions
Exercises
Application to Statistics
Self-Study Questions
Exercises
Projections: The Gram-Schmidt Process
The QR Decomposition
Uniqueness of the QR-factorization
True-False Questions
Exercises
Computer Projects
Exercises
Fourier Series: Scalar Product Spaces
Exercises
Computer Projects
Exercises
Orthogonal Matrices
Householder Matrices
True-False Questions
Exercises
Computer Projects
Exercises
Least Squares
Exercises
Computer Projects
Exercises
Quadratic Forms: Orthogonal Diagonalization
The Spectral Theorem
The Principal Axis Theorem
True-False Questions
Exercises
Computer Projects
Exercises
The Singular Value Decomposition (SVD)
Application of the SVD to Least-Squares Problems
True-False Questions
Exercises
Computing the SVD Using Householder Matrices
Diagonalizing Symmetric Matrices Using Householder Matrices
Hermitian Symmetric and Unitary Matrices
True-False Questions
Exercises
Chapter Summary
Generalized Eigenvectors
Generalized Eigenvectors
Exercises
Chain Bases
Jordan Form
True-False Questions
Exercises
The Cayley-Hamilton Theorem
Chapter Summary
Numerical Techniques
Condition Number
Norms
Condition Number
Least Squares
Exercises
Computing Eigenvalues
Iteration
The QR Method
Proof of Theorem 3
Exercises
Chapter Summary
Index

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