 # Linear Algebra and Its Applications ###### David C. Lay
Publisher:
Publication Date:
2006
Number of Pages:
112
Format:
Hardcover with CDROM
Edition:
3
Price:
0.00
ISBN:
0321287134
Category:
Textbook
We do not plan to review this book.

 Chapter 1  Linear Equations in Linear Algebra   INTRODUCTORY EXAMPLE: Linear Models in Economics and Engineering   1.1                   Systems of Linear Equations 1.2                   Row Reduction and Echelon Forms 1.3                   Vector Equations 1.4                   The Matrix Equation Ax = b 1.5                   Solution Sets of Linear Systems 1.6                   Applications of Linear Systems 1.7                   Linear Independence 1.8                   Introduction to Linear Transformations 1.9                   The Matrix of a Linear Transformation 1.10                 Linear Models in Business, Science, and Engineering         Supplementary Exercises   Chapter 2  Matrix Algebra   INTRODUCTORY EXAMPLE: Computer Models in Aircraft Design   2.1                   Matrix Operations 2.2                   The Inverse of a Matrix 2.3                   Characterizations of Invertible Matrices 2.4                   Partitioned Matrices 2.5                   Matrix Factorizations 2.6                   The Leontief Input=Output Model 2.7                   Applications to Computer Graphics 2.8                   Subspaces of R^n 2.9                   Dimension and Rank         Supplementary Exercises   Chapter 3  Determinants   INTRODUCTORY EXAMPLE: Determinants in Analytic Geometry   3.1                   Introduction to Determinants 3.2                   Properties of Determinants 3.3                   Cramer’s Rule, Volume, and Linear Transformations         Supplementary Exercises   Chapter 4  Vector Spaces   INTRODUCTORY EXAMPLE: Space Flight and Control Systems   4.1                   Vector Spaces and Subspaces 4.2                   Null Spaces, Column Spaces, and Linear Transformations 4.3                   Linearly Independent Sets; Bases 4.4                   Coordinate Systems 4.5                   The Dimension of a Vector Space 4.6                   Rank 4.7                   Change of Basis 4.8                   Applications to Difference Equations 4.9                   Applications to Markov Chains         Supplementary Exercises   Chapter 5  Eigenvalues and Eigenvectors   INTRODUCTORY EXAMPLE: Dynamical Systems and Spotted Owls   5.1                   Eigenvectors and Eigenvalues 5.2                   The Characteristic Equation 5.3                   Diagonalization 5.4                   Eigenvectors and Linear Transformations 5.5                   Complex Eigenvalues 5.6                   Discrete Dynamical Systems 5.7                   Applications to Differential Equations 5.8                   Iterative Estimates for Eigenvalues         Supplementary Exercises   Chapter 6  Orthogonality and Least Squares   INTRODUCTORY EXAMPLE: Readjusting the North American Datum   6.1                   Inner Product, Length, and Orthogonality 6.2                   Orthogonal Sets 6.3                   Orthogonal Projections 6.4                   The Gram-Schmidt Process 6.5                   Least-Squares Problems 6.6                   Applications to Linear Models 6.7                   Inner Product Spaces 6.8                   Applications of Inner Product Spaces         Supplementary Exercises   Chapter 7  Symmetric Matrices and Quadratic Forms   INTRODUCTORY EXAMPLE: Multichannel Image Processing   7.1                   Diagonalization of Symmetric Matrices 7.2                   Quadratic Forms 7.3                   Constrained Optimization 7.4                   The Singular Value Decomposition 7.5                   Applications to Image Processing and Statistics         Supplementary Exercises   ONLINE ONLY Chapter 8  The Geometry of Vector Spaces   INTRODUCTORY EXAMPLE: The Platonic Solids   8.1                   Affine Combinations 8.2                   Affine Independence 8.3                   Convex Combinations 8.4                   Hyperplanes 8.5                   Polytopes 8.6                   Curves and Surfaces         Supplementary Exercises   ONLINE ONLY Chapter 9  Optimization   INTRODUCTORY EXAMPLE: The Berlin Airlift   9.1                    Matrix Games 9.2                    Linear Programming — Geometric Method 9.3               Linear Programming — Simplex Method 9.4               Duality         Supplementary Exercises       Appendices   A                    Uniqueness of the Reduced Echelon Form B                    Complex Numbers   Glossary   Answers to Odd-Numbered Exercises   Index

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