| Description |
1 online resource |
| Contents |
Cover; Title Page; Copyright Page; About the Author; Dedication; Preface; CONTENTS; CHAPTER 1 Systems of Linear Equations and Matrices; 1.1 Introduction to Systems of Linear Equations; 1.2 Gaussian Elimination; 1.3 Matrices and Matrix Operations; 1.4 Inverses; Algebraic Properties of Matrices; 1.5 Elementary Matrices and a Method for Finding A-1; 1.6 More on Linear Systems and Invertible Matrices; 1.7 Diagonal, Triangular, and Symmetric Matrices; 1.8 Matrix Transformations; 1.9 Applications of Linear Systems; Network Analysis (Traffic Flow); Electrical Circuits; Balancing Chemical Equations |
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Polynomial Interpolation1.10 Application: Leontief Input-Output Models; CHAPTER 2 Determinants; 2.1 Determinants by Cofactor Expansion; 2.2 Evaluating Determinants by Row Reduction; 2.3 Properties of Determinants; Cramer's Rule; CHAPTER 3 Euclidean Vector Spaces; 3.1 Vectors in 2-Space, 3-Space, and n-Space; 3.2 Norm, Dot Product, and Distance in Rn; 3.3 Orthogonality; 3.4 The Geometry of Linear Systems; 3.5 Cross Product; CHAPTER 4 General Vector Spaces; 4.1 Real Vector Spaces; 4.2 Subspaces; 4.3 Linear Independence; 4.4 Coordinates and Basis; 4.5 Dimension; 4.6 Change of Basis |
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4.7 Row Space, Column Space, and Null Space4.8 Rank, Nullity, and the Fundamental Matrix Spaces; 4.9 Basic Matrix Transformations in R2 and R3; 4.10 Properties of Matrix Transformations; 4.11 Application: Geometry of Matrix Operators on R2; CHAPTER 5 Eigenvalues and Eigenvectors; 5.1 Eigenvalues and Eigenvectors; 5.2 Diagonalization; 5.3 Complex Vector Spaces; 5.4 Application: Differential Equations; 5.5 Application: Dynamical Systems and Markov Chains; CHAPTER 6 Inner Product Spaces; 6.1 Inner Products; 6.2 Angle and Orthogonality in Inner Product Spaces; 6.3 Gram-Schmidt Process |
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QR-Decomposition6.4 Best Approximation; Least Squares; 6.5 Application: Mathematical Modeling Using Least Squares; 6.6 Application: Function Approximation; Fourier Series; CHAPTER 7 Diagonalization and Quadratic Forms; 7.1 Orthogonal Matrices; 7.2 Orthogonal Diagonalization; 7.3 Quadratic Forms; 7.4 Optimization Using Quadratic Forms; 7.5 Hermitian, Unitary, and Normal Matrices; CHAPTER 8 General Linear Transformations; 8.1 General Linear Transformations; 8.2 Compositions and Inverse Transformations; 8.3 Isomorphism; 8.4 Matrices for General Linear Transformations; 8.5 Similarity |
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CHAPTER 9 Numerical Methods9.1 LU-Decompositions; 9.2 The Power Method; 9.3 Comparison of Procedures for Solving Linear Systems; 9.4 Singular Value Decomposition; 9.5 Application: Data Compression Using Singular Value Decomposition; CHAPTER 10 Applications of Linear Algebra; 10.1 Constructing Curves and Surfaces Through Specified Points; 10.2 The Earliest Applications of Linear Algebra; 10.3 Cubic Spline Interpolation; 10.4 Markov Chains; 10.5 Graph Theory; 10.6 Games of Strategy; 10.7 Leontief Economic Models; 10.8 Forest Management; 10.9 Computer Graphics |
| Notes |
Includes index |
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Print version record and CIP data provided by publisher; resource not viewed |
| Subject |
Algebras, Linear -- Textbooks
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Algebras, Linear.
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| Genre/Form |
Textbooks.
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| Form |
Electronic book
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| LC no. |
2013034443 |
| ISBN |
9781118800065 |
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1118800060 |
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