Linear Algebra and Its Applications / Edition 4 by David C. Lay | 9780321385178 | Hardcover | Barnes & Noble
Linear Algebra and Its Applications / Edition 4

Linear Algebra and Its Applications / Edition 4

2.7 10
by David C. Lay
     
 

ISBN-10: 0321385179

ISBN-13: 9780321385178

Pub. Date: 02/03/2011

Publisher: Pearson

NOTE: Before purchasing, check with your instructor to ensure you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, and registrations are not transferable. To register for and use Pearson's MyLab & Mastering products, you may also need a Course ID, which your instructor will

Overview

NOTE: Before purchasing, check with your instructor to ensure you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, and registrations are not transferable. To register for and use Pearson's MyLab & Mastering products, you may also need a Course ID, which your instructor will provide.

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With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a 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. These concepts are fundamental to the study of linear algebra, so students' understanding of them is vital to mastering the subject. This text makes these concepts more accessible by introducing them early in a familiar, concrete Rn setting, developing them gradually, and returning to them throughout the text so that when they are discussed in the abstract, students are readily able to understand.

Product Details

ISBN-13:
9780321385178
Publisher:
Pearson
Publication date:
02/03/2011
Edition description:
Older Edition
Pages:
576
Sales rank:
653,430
Product dimensions:
7.90(w) x 10.10(h) x 1.00(d)

Related Subjects

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.

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