ISBN 9781259025587,Introduction To Linear Algebra Nwith Applications

Introduction To Linear Algebra Nwith Applications

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ISBN 9781259025587
Publisher

Tata McGraw - Hill Education

Publication Year 2012
ISBN-13

ISBN 9781259025587

ISBN-10 1259025586
Binding

Paperback

Number of Pages 508 Pages
Language (English)
Subject

Linear algebra

This book provides the proper balance between computation, problem solving, and abstraction that will equip students with the necessary skills and problem solving strategies to allow for a greater understanding and appreciation of linear algebra and its numerous applications. About the Author Jim DeFranza Professor, Dept. of Mathematics, St. Lawrence University Daniel Gagliardi Asst. Professor, Dept. of Mathematics, SUNY Canton Table of Contents Chapter 1 Systems of Linear Equations and Matrices 1 1.1 Systems of Linear Equations Exercise Set 1.1 1.2 Matrices and Elementary Row Operations Exercise Set 1.2 1.3 Matrix Algebra Exercise Set 1.3 1.4 The Inverse of a Square Matrix Exercise Set 1.4 1.5 Matrix Equations Exercise Set 1.5 1.6 Determinants Exercise Set 1.6 1.7 Elementary Matrices and LU Factorization Exercise Set 1.7 1.8 Applications of Systems of Linear Equatio Exercise Set 1.8 Review Exercises Chapter Test Chapter 2 Linear Combinations and Linear Independence 2.1 Vectors in Rn Exercise Set 2.1 2.2 Linear Combinations Exercise Set 2.2 2.3 Linear Independence Exercise Set 2.3 Review Exercises Chapter Test Chapter 3 Vector Spaces 3.1 Definition of a Vector Space Exercise Set 3.1 3.2 Subspaces Exercise Set 3.2 3.3 Basis and Dimension Exercise Set 3.3 3.4 Coordinates and Change of Basis Exercise Set 3.4 3.5 Application: Differential Equations Exercise Set 3.5 Review Exercises Chapter Test Chapter 4 Linear Transformations 4.1 Linear Transformations Exercise Set 4.1 4.2 The Null Space and Range Exercise Set 4.2 4.3 Isomorphisms Exercise Set 4.3 4.4 Matrix Representation of a Linear Transformation Exercise Set 4.4 4.5 Similarity Exercise Set 4.5 4.6 Application : Computer Graphics Exercise Set 4.6 Review Exercises Chapter Test Chapter 5 Eigenvalues and Eigenvectors 5.1 Eigenvalues and Eigenvectors Exercise Set 5.1 5.2 Diagonalization Exercise Set 5.2 5.3 Application : Systems of Linear Different Exercise Set 5.3 5.4 Application : Markov Chains Exercise Set 5.4 Review Exercises Chapter Test Chapter 6 Inner Product Spaces 6.1 The Dot Product on Rn Exercise Set 6.1 6.2 Inner Product Spaces Exercise Set 6.2 6.3 Orthonormal Bases Exercise Set 6.3 6.4 Orthogonal Complements Exercise Set 6.4 6.5 Application : Least Squares Approximation Exercise Set 6.5 6.6 Diagonalization of Symmetric Matrices Exercise Set 6.6 6.7 Application : Quadratic Forms Exercise Set 6.7 6.8 Application : Singular Value Decomposition Exercise Set 6.8 Review Exercises Chapter Test A Preliminaries A.1 Algebra of Sets Exercise Set A.1 A.2 Functions Exercise Set A.2 A.3 Techniques of Proof Exercise Set A.3 A.4 Mathematical Induction Exercise Set A.4 Answers to Odd-Numbered Exercises A.3 Techniques of Proof Exercise Set A.3 A.4 Mathematical Induction Exercise Set A.4 Answers to Odd-Numbered Exercises