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Note: Each chapter concludes with a Chapter Summary, Review Exercises, and Projects. What Is Linear Algebra? | |
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Systems of Linear Equations Biographical Sketch of Carl Friedrich Gauss | |
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Introduction to Systems of Linear Equations | |
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Gaussian Elimination and Gauss-Jordan Elimination | |
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Applications of Systems of Linear Equations | |
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Matrices Biographical Sketch of Arthur Cayley | |
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Operations with Matrices | |
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Properties of Matrix Operations | |
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The Inverse of a Matrix | |
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Elementary Matrices | |
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Applications of Matrix Operations | |
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Determinants Biographical Sketch of Augustin-Louis Cauchy | |
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The Determinant of a Matrix | |
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Evaluation of a Determinant Using Elementary Operations | |
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Properties of Determinants | |
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Introduction to Eigenvalues | |
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Applications of Determinants Cumulative Test for Chapters 13 | |
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Vector Spaces Biographical Sketch of William Rowan Hamilton | |
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Vectors in Rn | |
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Vector Spaces | |
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Subspaces of Vector Spaces | |
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Spanning Sets and Linear Independence | |
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Basis and Dimension | |
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Rank of a Matrix and Systems of Linear Equations | |
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Coordinates and Change of Basis | |
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Applications of Vector Spaces | |
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Inner Product Spaces Biographical Sketch of Jean-Baptiste Joseph Fourier | |
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Length and Dot Product in Rn | |
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Inner Product Spaces | |
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Orthonormal Bases: Gram-Schmidt Process | |
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Mathematical Models and Least Squares Analysis | |
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Applications of Inner Product Spaces Cumulative Test for Chapters 4 and 5 | |
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Linear Transformations Biographical Sketch of Emmy Noether | |
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Introduction to Linear Transformations | |
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The Kernel and Range of a Linear Transformation | |
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Matrices for Linear Transformations | |
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Transition Matrices and Similarity | |
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Applications of Linear Transformations | |
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Eigenvalues and Eigenvectors Biographical Sketch of James Joseph Sylvester | |
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Eigenvalues and Eigenvectors | |
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Diagonalization | |
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Symmetric Matrices and Orthogonal Diagonalization | |
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Applications of Eigenvalues and Eigenvectors Cumulative Test for Chapters 6 and 7 | |
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Complex Vector Spaces* Biographical Sketch of Charles Hermite | |
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Complex Numbers | |
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Conjugates and Division of Complex Numbers | |
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Polar Form and DeMoivre's Theorem | |
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Complex Vector Spaces and Inner Products | |
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Unitary and Hermitian Matrices | |
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Linear Programming* Biographical Sketch of John von Neumann | |
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Systems of Linear Inequalities | |
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Linear Programming Involving Two Variables | |
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The Simplex Method: Maximization | |
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The Simplex Method: Minimization | |
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The Simplex Method: Mixed Constraints | |
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Numerical Methods | |
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Biographical Sketch of Carl Gustav Jacob Jacobi | |
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Gaussian Elimination with Partial Pivoting | |
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Interative Methods for Solving Linear Systems | |
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Power Method for Approximating Eigenvalues | |
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Applications of Numerical Methods | |
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Appendices | |
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Mathematical Induction and Other Forms of Proofs | |
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Computer Algebra Systems and Graphing Calculators | |
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Answer Key Index * Chapters 8, 9, and 10 are available on the Learning Tools Student CD-ROM and the textbook web site | |