chapter Part I. Linear Algebra -- chapter Basic Linear Algebra -- chapter 1 Vectors, Matrices, and Systems of Linear Equations -- chapter 2 Linear Independence, Span, and Bases -- chapter 3 Linear Transformations -- chapter 4 Determinants and Eigenvalues -- chapter 5 Inner Product Spaces, Orthogonal Projection, Least Squares, and Singular Value Decomposition -- chapter Matrices with Special Properties -- chapter 6 Canonical Forms -- chapter 7 Unitary Similarity, Normal Matrices, and Spectral Theory -- chapter 8 Hermitian and Positive Definite Matrices -- chapter 9 Nonnegative Matrices and Stochastic Matrices -- chapter 10 Partitioned Matrices -- chapter Advanced Linear Algebra -- chapter 11 Functions of Matrices -- chapter 12 Quadratic, Bilinear, and Sesquilinear Forms -- chapter 13 Multilinear Algebra -- chapter 14 Matrix Equalities and Inequalities -- chapter 15 Matrix Perturbation Theory -- chapter 16 Pseudospectra -- chapter 17 Singular Values and Singular Value Inequalities -- chapter 18 Numerical Range -- chapter 19 Matrix Stability and Inertia -- chapter Topics in Advanced Linear Algebra -- chapter 20 Inverse Eigenvalue Problems -- chapter 21 Totally Positive and Totally Nonnegative Matrices -- chapter 22 Linear Preserver Problems -- chapter 23 Matrices over Integral Domains -- chapter 24 Similarity of Families of Matrices -- chapter 25 Max-Plus Algebra -- chapter 26 Matrices Leaving a Cone Invariant -- chapter Part II. Combinatorial Matrix Theory and Graphs -- chapter Martices and Graphs -- chapter 27 Combinatorial Matrix Theory -- chapter 28 Matrices and Graphs -- chapter 29 Digraphs and Matrices -- chapter 30 Bipartite Graphs and Matrices -- chapter Topics in Combinatorial Matrix Theory -- chapter 31 Permanents -- chapter 32 D-Optimal Matrices -- chapter 33 Sign Pattern Matrices -- chapter 34 Multiplicity Lists for the Eigenvalues of Symmetric Matrices with a Given Graph -- chapter 35 Matrix Completion Problems -- chapter 36 Algebraic Connectivity -- chapter Part III. Numerical Methods -- chapter Numerical Methods for Linear Systems -- chapter 37 Vector and Matrix Norms, Error Analysis, Efficiency, and Stability -- chapter 38 Matrix Factorizations and Direct Solution of Linear Systems -- chapter 39 Least Squares Solution of Linear Systems -- chapter 40 Sparse Matrix Methods -- chapter 41 Iterative Solution Methods for Linear Systems -- chapter Numerical Methods for Eigenvalues -- chapter 42 Symmetric Matrix Eigenvalue Techniques -- chapter 43 Unsymmetric Matrix Eigenvalue Techniques -- chapter 44 The Implicitly Restarted Arnoldi Methods -- chapter 45 Computation of the Singular Value Decomposition -- chapter 46 Computing Eigenvalues and Singular Values to High Relative Accuracy -- chapter Computational Linear Algebra -- chapter 47 Fast Matrix Multiplication -- chapter 48 Structured Matrix Computations -- chapter 49 Large-Scale Matrix Computations -- chapter Part IV. Applications -- chapter Applications to Optimization -- chapter 50 Linear Programming -- chapter 51 Semidefinite Programming -- chapter Applications to Probability and Statistics -- chapter 52 Random Vectors and Linear Statistical Models -- chapter 53 Multivariate Statistical Analysis -- chapter 54 Markov Chains -- chapter Applications to Analysis -- chapter 55 Differential Equations and Stability -- chapter 56 Dynamical Systems and Linear Algebra -- chapter 57 Control Theory -- chapter 58 Fourier Analysis -- chapter Applications to Physical and Biological Sciences -- chapter 59 Linear Algebra and Mathematical Physics -- chapter 60 Linear Algebra in Biomolecular Modeling -- chapter Applications to Computer Science -- chapter 61 Coding Theory -- chapter 62 Quantum Computation -- chapter 63 Information Retrieval and Web Search -- chapter Chapte 64. Signal Processing -- chapter Applications to Geometry -- chapter 65 Geometry -- chapter 66 Some Applications of Matrices and Graphs in Euclidean Geometry -- chapter Applications to Algebra -- chapter 67 Matrix Groups -- chapter 68 Group Representations -- chapter 69 Nonassociative Algebras -- chapter 70 Lie Algebras -- chapter Part V. Computational Software -- chapter Interactive Software for Linear Algebra -- chapter 71 Matlab -- chapter 72 Linear Algebra in Maple -- chapter 73 Mathematica -- chapter Packages of Subroutines for Linear Algebra -- chapter 74 BLAS -- chapter 75 LAPACK / chapter 76 Use of ARPACK and EIGS -- chapter 77 Summary of Software for Linear Algebra Freely Available on the Web.