Linear Algebra A Modern Introduction

ISBN-10: 0534998585

ISBN-13: 9780534998585

Edition: 2nd 2006 (Student Manual, Study Guide, etc.)

Authors: David Poole
List price: $109.95
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Description: By Robert Rogers of Bay State College. Provides detailed and complete solutions to the odd-numbered exercises and test questions; section and chapter summaries of symbols, definitions, and theorems; study tips and hints. Complex exercises are explored through a question-and-answer format designed to deepen understanding. Challenging and entertaining problems that further explore selected exercises are also included.

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Book details

List price: $109.95
Edition: 2nd
Copyright year: 2006
Publisher: Delmar Cengage Learning
Publication date: 7/22/2005
Binding: Paperback
Pages: 592
Size: 7.25" wide x 9.50" long x 1.00" tall
Weight: 1.782
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, Dr. Poole was Trent University's Associate Dean (Teaching & Learning). His research interests include discrete mathematics, ring theory, and mathematics education. He received his B.Sc. from Acadia University in 1976 before earning his M.Sc. (1977) and Ph.D. (1984) from McMaster University. When he is not doing mathematics, David Poole enjoys hiking and cooking, and he is an avid film buff.

Vectors
The Geometry and Algebra of Vectors
Length and Angle: The Dot Product
Exploration: Vectors and Geometry
Lines and Planes
Exploration: The Cross Product
Code Vectors and Modular Arithmetic
Chapter 1 Review
Systems of Linear Equations
Introduction to Systems of Linear Equations
Exploration: Lies My Computer Told Me
Direct Methods for Solving Linear Systems
Exploration: Partial Pivoting
Exploration: An Introduction to the Analysis of Algorithms
Spanning Sets and Linear Independence
Applications
Iterative Methods for Solving Linear Systems
Chapter 2 Review
Matrices
Matrix Operations
Matrix Algebra
The Inverse of a Matrix
The LU Factorization
Subspaces, Basis, Dimension, and Rank
Introduction to Linear Transformations
Applications
Chapter 3 Review
Eigenvalues and Eigenvectors
Introduction to Eigenvalues and Eigenvectors
Determinants
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
Chapter 4 Review
Orthogonality
Orthogonality in Rn
Orthogonal Complements and 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
Chapter 5 Review
Vector Spaces
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 Crystallographic Restriction
Applications
Chapter 6 Review
Distance and Approximation
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
Applications
Chapter 7 Review
Key Definitions and Concepts
Theorems
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