Cover image for Linear algebra and its applications
Title:
Linear algebra and its applications
Personal Author:
Edition:
2nd updated ed.
Publication Information:
Reading, Massachusetts : Addison-Wesley Longman, 1999
Physical Description:
1v. + 1 CD-ROM (CP 1122)
ISBN:
9780201347746
Subject Term:

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Summary

Summary

Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text. Finally, when discussed in the abstract, these concepts are more accessible. Students conceptual understanding is reinforced through True/False questions, practice problems, and the use of technology. David Lay changed the study of linear algebra with the execution of this philosophy, and continues his quest to improve the way linear algebra is taught with the new Updated Second Edition. With this update he takes the instruction of linear algebra to a new level through inc


Table of Contents

(Each chapter begins with an Introductory Example and ends with Supplementary Exercises.)
1 Linear Equations In Linear Algebra
Introductory Example: Linear Models in Economics and Engineering
Systems of Linear Equations
Row Reduction and Echelon Forms
Vector Equations
The Matrix Equation Ax = b
Solution Sets of Linear Systems
Linear Independence
Introduction to Linear Transformations
The Matrix of a Linear Transformation
Linear Models in Business, Science, and Engineering
Supplementary Exercises
2 Matrix Algebra
Introductory Example: Computer Graphics in Automotive Design
Matrix Operations
The Inverse of a Matrix
Characterizations of Invertible Matrices
Partitioned Matrices
Matrix Factorizations
Iterative Solutions of Linear Systems
The Leontief Input-Output Model
Applications to Computer Graphics
Subspaces of Rn
Supplementary Exercises
3 Determinants
Introductory Example: Determinants in Analytic Geometry
Introduction to Determinants
Properties of Determinants
Cramer?s Rule, Volume, and Linear Transformations
Supplementary Exercises
4 Vector Spaces
Introductory Example: Space Flight and Control Systems
Vector Spaces and Subspaces
Null Spaces, Column Spaces, and Linear Transformations
Linearly Independent Sets; Bases
Coordinate Systems
The Dimension of a Vector Space
Rank
Change of Basis
Applications to Difference Equations
Applications to Markov Chains
Supplementary Exercises
5 Eigenvalues and Eigenvectors
Introductory Example: Dynamical Systems and Spotted Owls
Eigenvectors and Eigenvalues
The Characteristic Equation
Diagonalization
Eigenvectors and Linear Transformations
Complex Eigenvalues
Discrete Dynamical Systems
Applications to Differential Equations
Iterative Estimates for Eigenvalues
Supplementary Exercises
6 Orthogonality and Least-Squares
Introductory Example: Readjusting the North American Datum
Inner Product, Length, and Orthogonality
Orthogonal Sets
Orthogonal Projections
The Gram-Schmidt Process
Least-Squares Problems
Applications to Linear Models
Inner Product Spaces
Applications of Inner Product Spaces
Supplementary Exercises
7 Symmetric Matrices and Quadratic Forms
Introductory Example: Multichannel Image Processing
Diagonalization of Symmetric Matrices
Quadratic Forms
Constrained Optimization
The Singular Value Decomposition
Applications to Image Processing and Statistics
Supplementary Exercises
Appendices
Uniqueness of the Reduced Echelon Form
Complex Numbers
Glossary
Answers to Odd-Numbered Exercises
Index