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Note: Each chapter concludes with a Chapter Summary, Review Exercises, and Projects. What Is Linear Algebra? | |
Systems of Linear Equations Biographical Sketch of Carl Friedrich Gauss | |
Introduction to Systems of Linear Equations | |
Gaussian Elimination and Gauss-Jordan Elimination | |
Applications of Systems of Linear Equations | |
Matrices Biographical Sketch of Arthur Cayley | |
Operations with Matrices | |
Properties of Matrix Operations | |
The Inverse of a Matrix | |
Elementary Matrices | |
Applications of Matrix Operations | |
Determinants Biographical Sketch of Augustin-Louis Cauchy | |
The Determinant of a Matrix | |
Evaluation of a Determinant Using Elementary Operations | |
Properties of Determinants | |
Introduction to Eigenvalues | |
Applications of Determinants Cumulative Test for Chapters 1–3 | |
Vector Spaces Biographical Sketch of William Rowan Hamilton | |
Vectors in Rn | |
Vector Spaces | |
Subspaces of Vector Spaces | |
Spanning Sets and Linear Independence | |
Basis and Dimension | |
Rank of a Matrix and Systems of Linear Equations | |
Coordinates and Change of Basis | |
Applications of Vector Spaces | |
Inner Product Spaces Biographical Sketch of Jean-Baptiste Joseph Fourier | |
Length and Dot Product in Rn | |
Inner Product Spaces | |
Orthonormal Bases: Gram-Schmidt Process | |
Mathematical Models and Least Squares Analysis | |
Applications of Inner Product Spaces Cumulative Test for Chapters 4 and 5 | |
Linear Transformations Biographical Sketch of Emmy Noether | |
Introduction to Linear Transformations | |
The Kernel and Range of a Linear Transformation | |
Matrices for Linear Transformations | |
Transition Matrices and Similarity | |
Applications of Linear Transformations | |
Eigenvalues and Eigenvectors Biographical Sketch of James Joseph Sylvester | |
Eigenvalues and Eigenvectors | |
Diagonalization | |
Symmetric Matrices and Orthogonal Diagonalization | |
Applications of Eigenvalues and Eigenvectors Cumulative Test for Chapters 6 and 7 | |
Complex Vector Spaces* Biographical Sketch of Charles Hermite | |
Complex Numbers | |
Conjugates and Division of Complex Numbers | |
Polar Form and DeMoivre's Theorem | |
Complex Vector Spaces and Inner Products | |
Unitary and Hermitian Matrices | |
Linear Programming* Biographical Sketch of John von Neumann | |
Systems of Linear Inequalities | |
Linear Programming Involving Two Variables | |
The Simplex Method: Maximization | |
The Simplex Method: Minimization | |
The Simplex Method: Mixed Constraints | |
Numerical Methods | |
Biographical Sketch of Carl Gustav Jacob Jacobi | |
Gaussian Elimination with Partial Pivoting | |
Interative Methods for Solving Linear Systems | |
Power Method for Approximating Eigenvalues | |
Applications of Numerical Methods | |
Appendices | |
Mathematical Induction and Other Forms of Proofs | |
Computer Algebra Systems and Graphing Calculators | |
Answer Key Index * Chapters 8, 9, and 10 are available on the Learning Tools Student CD-ROM and the textbook web site | |
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