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Elementary Linear Algebra 6th Edition by Ron Larson, David C Falvo, Bruce H Edwards ISBN 0618783768 9780618783762

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ISBN 10: 0618783768
ISBN 13: 9780618783762
Author: Ron Larson, David C Falvo, Bruce H Edwards

the Cornerstone Of Elementary Linear Algebra Is The Authors’ Clear, Careful, And Concise Presentation Of Material—written So That Students Can Fully Understand How Mathematics Works. This Program Balances Theory With Examples, Applications, And Geometric Intuition For A Complete, Step-by-step Learning System.the Sixth Edition Incorporates Up-to-date Coverage Of Computer Algebra Systems (maple/matlab/mathematica); Additional Support Is Provided In A Corresponding Technology Guide. Data And Applications Also Reflect Current Statistics And Examples To Engage Students And Demonstrate The Link Between Theory And Practice.

Elementary Linear Algebra 6th Edition Table of contents:

WHAT IS LINEAR ALGEBRA?
1.1 Introduction to Systems of Linear Equations
1.2 Gaussian Elimination and Gauss-Jordan Elimination
1.3 Applications of Systems of Linear Equations
Project 1 Graphing Linear Equations
Project 2 Underdetermined and Overdetermined Systems of Equations

2. Matrices
2.1 Operations with Matrices
2.2 Properties of Matrix Operations
2.3 The Inverse of a Matrix
2.4 Elementary Matrices
2.5 Applications of Matrix Operations
Project 1 Exploring Matrix Multiplication
Project 2 Nilpotent Matrices

3. Determinants and Eigenvalues
3.1 The Determinant of a Matrix
3.2 Evaluation of a Determinant Using Elementary Operations
3.3 Properties of Determinants
3.4 Introduction to Eigenvalues
3.5 Applications of Determinants
Project 1 Eigenvalues and Stochastic Matrices
Project 2 The Cayley-Hamilton Theorem
Cumulative Test for Chapters 1–3

4. Vector Spaces
4.1 Vectors in Rⁿ
4.2 Vector Spaces
4.3 Subspaces of Vector Spaces
4.4 Spanning Sets and Linear Independence
4.5 Basis and Dimension
4.6 Rank of a Matrix and Systems of Linear Equations
4.7 Coordinates and Change of Basis
4.8 Applications of Vector Spaces
Project 1 Solutions of Linear Systems
Project 2 Direct Sum

5. Inner Product Spaces
5.1 Length and Dot Product in Rⁿ
5.2 Inner Product Spaces
5.3 Orthonormal Bases: Gram-Schmidt Process
5.4 Mathematical Models and Least Squares Analysis
5.5 Applications of Inner Product Spaces
Project 1 The QR-Factorization
Project 2 Orthogonal Matrices and Change of Basis
Cumulative Test for Chapters 4 and 5

6. Linear Transformations
6.1 Introduction to Linear Transformations
6.2 The Kernel and Range of a Linear Transformation
6.3 Matrices for Linear Transformations
6.4 Transition Matrices and Similarity
6.5 Applications of Linear Transformations
Project 1 Reflections in the Plane (I)
Project 2 Reflections in the Plane (II)

7. Eigenvalues and Diagonalization
7.1 Eigenvalues and Eigenvectors
7.2 Diagonalization
7.3 Symmetric Matrices and Orthogonal Diagonalization
7.4 Applications of Eigenvalues and Eigenvectors
Project 1 Population Growth and Dynamical Systems (I)
Project 2 The Fibonacci Sequence
Cumulative Test for Chapters 6 and 7

Appendix
Mathematical Induction and Other Forms of Proofs

Answer Key
Index

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Tags: Ron Larson, David C Falvo, Bruce H Edwards, Elementary Linear Algebra