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Linear Algebra A Modern Introduction

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ISBN-10: 0538735457

ISBN-13: 9780538735452

Edition: 3rd 2011

Authors: David Poole

List price: $350.95
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Book details

List price: $350.95
Edition: 3rd
Copyright year: 2011
Publisher: Brooks/Cole
Publication date: 5/25/2010
Binding: Hardcover
Pages: 768
Size: 8.00" wide x 10.00" long x 1.25" tall
Weight: 3.652
Language: English

David Poole is Professor of Mathematics at Trent University, where he has been a faculty member since 1984. Dr. Poole has won numerous teaching awards: Trent University's Symons Award for Excellence in Teaching (the university's top teaching award), three merit awards for teaching excellence, a 2002 Ontario Confederation of University Faculty Associations Teaching Award (the top university teaching award in the province), a 2003 3M Teaching Fellowship (the top university teaching award in Canada, sponsored by 3M Canada Ltd.), a 2007 Leadership in Faculty Teaching Award from the province of Ontario, and the Canadian Mathematical Society's 2009 Excellence in Teaching Award. From 2002-2007,…    

Introduction: The Racetrack Game
The Geometry and Algebra of Vectors
Length and Angle: The Dot Product
Exploration: Vectors and Geometry
Lines and Planes
Exploration: The Cross Product
Applications: Force Vectors
Code Vectors
Vignette: The Codabar System
Systems of Linear Equations
Introduction: Triviality
Introduction to Systems of Linear Equations
Direct Methods for Solving Linear Systems
Exploration: Lies My Computer Told Me
Exploration: Partial Pivoting
Exploration: Counting Operations: An Introduction to the Analysis of Algorithms
Spanning Sets and Linear Independence
Applications: Allocation of Resources
Balancing Chemical Equations
Network Analysis
Electrical Networks
Linear Economic Models
Finite Linear Games
Vignette: The Global Positioning System
Iterative Methods for Solving Linear Systems
Introduction: Matrices in Action
Matrix Operations
Matrix Algebra
The Inverse of a Matrix
The LU Factorization
Subspaces, Basis, Dimension, and Rank
Introduction to Linear Transformations
Vignette: Robotics
Applications: Markov Chains
Linear Economic Models
Population Growth
Graphs and Digraphs
Error-Correcting Codes.
Eigenvalues and Eigenvectors
Introduction: A Dynamical System on Graphs
Introduction to Eigenvalues and Eigenvectors
Vignette: Lewis Carroll's Condensation Method
Exploration: Geometric Applications of Determinants
Eigenvalues and Eigenvectors of n x n Matrices
Similarity and Diagonalization
Iterative Methods for Computing Eigenvalues
Applications and the Perron-Frobenius Theorem: Markov Chains
Population Growth
The Perron-Frobenius Theorem
Linear Recurrence Relations
Systems of Linear Differential Equations
Discrete Linear Dynamical Systems
Vignette: Ranking Sports Teams and Searching the Internet
Introduction: Shadows on a Wall
Orthogonality in Rn
Orthogonal Complements and Orthogonal Projections
The Gram-Schmidt Process and the QR Factorization
Exploration: The Modified QR Factorization
Exploration: Approximating Eigenvalues with the QR Algorithm
Orthogonal Diagonalization of Symmetric Matrices
Applications: Dual Codes
Quadratic Forms
Graphing Quadratic Equations
Vector Spaces
Introduction: Fibonacci in (Vector) Space
Vector Spaces and Subspaces
Linear Independence, Basis, and Dimension
Exploration: Magic Squares
Change of Basis
Linear Transformations
The Kernel and Range of a Linear Transformation
The Matrix of a Linear Transformation
Exploration: Tilings, Lattices and the Crystallographic Restriction
Applications: Homogeneous Linear Differential Equations
Linear Codes
Distance and Approximation
Introduction: Taxicab Geometry
Inner Product Spaces
Exploration: Vectors and Matrices with Complex Entries
Exploration: Geometric Inequalities and Optimization Problems
Norms and Distance Functions
Least Squares Approximation
The Singular Value Decomposition
Vignette: Digital Image Compression
Applications: Approximation of Functions
Error-Correcting Codes
Mathematical Notation and Methods of Proof
Mathematical Induction
Complex Numbers