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Summary: The hallmark of this text has been the authors' clear, careful, and concise presentation of linear algebra so that students can fully understand how the mathematics works. The text balances theory with examples, applications, and geometric intuition.Edition/Copyright: 5TH 04
Larson, Ron : The Pennsylvania State University, The Behrend College
Edwards, Bruce H. : University of Florida
Note: Each chapter concludes with a Chapter Summary, Review Exercises, and Projects.
What Is Linear Algebra?
1. Systems of Linear Equations
Biographical Sketch of Carl Friedrich Gauss
1.1 Introduction to Systems of Linear Equations
1.2 Gaussian Elimination and Gauss-Jordan Elimination
1.3 Applications of Systems of Linear Equations
Biographical Sketch of Arthur Cayley
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
Biographical Sketch of Augustin-Louis Cauchy
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
Cumulative Test for Chapters 1-3
4. Vector Spaces
Biographical Sketch of William Rowan Hamilton
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
5. Inner Product Spaces
Biographical Sketch of Jean-Baptiste Joseph Fourier
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
Cumulative Test for Chapters 4 and 5
6. Linear Transformations
Biographical Sketch of Emmy Noether
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
7. Eigenvalues and Eigenvectors
Biographical Sketch of James Joseph Sylvester
7.1 Eigenvalues and Eigenvectors
7.3 Symmetric Matrices and Orthogonal Diagonalization
7.4 Applications of Eigenvalues and Eigenvectors
Cumulative Test for Chapters 6 and 7
8. Complex Vector Spaces
Biographical Sketch of Charles Hermite
8.1 Complex Numbers
8.2 Conjugates and Division of Complex Numbers
8.3 Polar Form and DeMoivre's Theorem
8.4 Complex Vector Spaces and Inner Products
8.5 Unitary and Hermitian Matrices
9. Linear Programming
Biographical Sketch of John von Neumann
9.1 Systems of Linear Inequalities
9.2 Linear Programming Involving Two Variables
9.3 The Simplex Method: Maximization
9.4 The Simplex Method: Minimization
9.5 The Simplex Method: Mixed Constraints
10. Numerical Methods
Biographical Sketch of Carl Gustav Jacob Jacobi
10.1 Gaussian Elimination with Partial Pivoting
10.2 Interative Methods for Solving Linear Systems
10.3 Power Method for Approximating Eigenvalues
10.4 Applications of Numerical Methods
A. Mathematical Induction and Other Forms of Proofs
B. Computer Algebra Systems and Graphing Calculators
Chapters 8, 9, and 10 are available on the Learning Tools Student CD-ROM and the textbook web site.
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