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 Chapter 1. Preliminaries
  1.1. Vector Spaces
  1.2. Bases and Coordinates
  1.3. Linear Transformations
  1.4. Matrices
  1.5. The Matrix of a Linear Transformation
  1.6. Change of Basis and Similarity
  1.7. Transposes
  1.8. Special Types of Matrices
  1.9. Submatrices, Partitioned Matrices, and Block Multiplication
  1.10. Invariant Subspaces
  1.11. Determinants
  1.12. Tensor Products
  Exercises
 Chapter 2. Inner Product Spaces and Orthogonality
  2.1. The Inner Product
  2.2. Length, Orthogonality, and Projection onto a Line
  2.3. Inner Products in Cn
  2.4. Orthogonal Complements and Projection onto a Subspace
  2.5. Hilbert Spaces and Fourier Series
  2.6. Unitary Tranformations
  2.7. The Gram–Schmidt Process and QR Factorization
  2.8. Linear Functionals and the Dual Space
  Exercises
 Chapter 3. Eigenvalues, Eigenvectors, Diagonalization, and Triangularization
  3.1. Eigenvalues
  3.2. Algebraic and Geometric Multiplicity
  3.3. Diagonalizability
  3.4. A Triangularization Theorem
  3.5. The Gerˇsgorin Circle Theorem
  3.6. More about the Characteristic Polynomial
  3.7. Eigenvalues of AB and BA
  Exercises
 Chapter 4. The Jordan and Weyr Canonical Forms
  4.1. A Theorem of Sylvester and Reduction to Block Diagonal Form
  4.2. Nilpotent Matrices
  4.3. The Jordan Form of a General Matrix
  4.4. The Cayley–Hamilton Theorem and the Minimal Polynomial
  4.5. Weyr Normal Form
  Exercises
 Chapter 5. Unitary Similarity and Normal Matrices
  5.1. Unitary Similarity
  5.2. Normal Matrices—the Spectral Theorem
  5.3. More about Normal Matrices
  5.4. Conditions for Unitary Similarity
  Exercises
 Chapter 6. Hermitian Matrices
  6.1. Conjugate Bilinear Forms
  6.2. Properties of Hermitian Matrices and Inertia
  6.3. The Rayleigh–Ritz Ratio and the Courant–Fischer Theorem
  6.4. Cauchy’s Interlacing Theorem and Other Eigenvalue Inequalities
  6.5. Positive Definite Matrices
  6.6. Simultaneous Row and Column Operations
  6.7. Hadamard’s Determinant Inequality
  6.8. Polar Factorization and Singular Value Decomposition
  Exercises
 Chapter 7. Vector and Matrix Norms
  7.1. Vector Norms
  7.2. Matrix Norms
  Exercises
 Chapter 8. Some Matrix Factorizations
  8.1. Singular Value Decomposition
  8.2. Householder Transformations
  8.3. Using Householder Transformations to Get Triangular, Hessenberg, and Tridiagonal Forms
  8.4. Some Methods for Computing Eigenvalues
  8.5. LDU Factorization
  Exercises
 Chapter 9. Field of Values
  9.1. Basic Properties of the Field of Values
  9.2. The Field of Values for Two-by-Two Matrices
  9.3. Convexity of the Numerical Range
  Exercises
 Chapter 10. Simultaneous Triangularization
  10.1. Invariant Subspaces and Block Triangularization
  10.2. Simultaneous Triangularization, Property P, and Commutativity
  10.3. Algebras, Ideals, and Nilpotent Ideals
  10.4. McCoy’s Theorem
  10.5. Property L
  Exercises
 Chapter 11. Circulant and Block Cycle Matrices
  11.1. The J Matrix
  11.2. Circulant Matrices
  11.3. Block Cycle Matrices
  Exercises
 Chapter 12. Matrices of Zeros and Ones
  12.1. Introduction: Adjacency Matrices and Incidence Matrices
  12.2. Basic Facts about (0, 1)-Matrices
  12.3. The Minimax Theorem of K¨onig and Egerv´ary
  12.4. SDRs, a Theorem of P. Hall, and Permanents
  12.5. Doubly Stochastic Matrices and Birkhoff’s Theorem
  12.6. A Theorem of Ryser
  Exercises
 Chapter 13. Block Designs
  13.1. t-Designs
  13.2. Incidence Matrices for 2-Designs
  13.3. Finite Projective Planes
  13.4. Quadratic Forms and the Witt Cancellation Theorem
  13.5. The Bruck–Ryser–Chowla Theorem
  Exercises
 Chapter 14. Hadamard Matrices
  14.1. Introduction
  14.2. The Quadratic Residue Matrix and Paley’s Theorem
  14.3. Results of Williamson
  14.4. Hadamard Matrices and Block Designs
  14.5. A Determinant Inequality, Revisited
  Exercises
 Chapter 15. Graphs
  15.1. Definitions
  15.2. Graphs and Matrices
  15.3. Walks and Cycles
  15.4. Graphs and Eigenvalues
  15.5. Strongly Regular Graphs
  Exercises
 Chapter 16. Directed Graphs
  16.1. Definitions
  16.2. Irreducibility and Strong Connectivity
  16.3. Index of Imprimitivity
  16.4. Primitive Graphs
  Exercises
 Chapter 17. Nonnegative Matrices
  17.1. Introduction
  17.2. Preliminaries
  17.3. Proof of Perron’s Theorem
  17.4. Nonnegative Matrices
  17.5. Irreducible Matrices
  17.6. Primitive and Imprimitive Matrices
  Exercises
 Chapter 18. Error-Correcting Codes
  18.1. Introduction
  18.2. The Hamming Code
  18.3. Linear Codes: Parity Check and Generator Matrices
  18.4. The Hamming Distance
  18.5. Perfect Codes and the Generalized Hamming Code
  18.6. Decoding
  18.7. Codes and Designs
  18.8. Hadamard Codes
  Exercises
 Chapter 19. Linear Dynamical Systems
  19.1. Introduction
  19.2. A Population Cohort Model
  19.3. First-Order, Constant Coefficient, Linear Differential and Difference Equations
  19.4. Constant Coefficient, Homogeneous Systems
  19.5. Constant Coefficient, Nonhomogeneous Systems; Equilibrium Points
  19.6. Nonnegative Systems
  19.7. Markov Chains
 Exercises
 Bibliography
 Index