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| Preface | |
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| Basic concepts of matrix theory | |
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| Matrices | |
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| Determinants | |
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| Nonsingular matrices. Inverse matrices | |
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| Schur complement. Factorization | |
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| Vector spaces. Rank | |
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| Eigenvectors, eigenvalues. Characteristic polynomial | |
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| Similarity. Jordan normal form | |
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| Symmetric Matrices. Positive Definite and Semidefinite Matrices | |
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| Euclidean and unitary spaces | |
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| Symmetric and Hermitian matrices | |
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| Orthogonal, unitary matrices | |
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| Gram-Schmidt orthonormalization | |
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| Positive definite matrices | |
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| Sylvester's law of inertia | |
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| Singular value decomposition | |
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| Graphs and Matrices | |
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| Digraphs | |
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| Digraph of a matrix | |
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| Undirected graphs. Trees | |
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| Bigraphs | |
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| Nonnegative Matrices. Stochastic and Doubly Stochastic Matrices | |
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| Nonnegative matrices | |
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| The Perron-Frobenius theorem | |
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| Cyclic matrices | |
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| Stochastic matrices | |
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| Doubly stochastic matrices | |
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| M-Matrices (Matrices of Classes K and K[subscript 0]) | |
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| Class K | |
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| Class K[subscript 0] | |
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| Diagonally dominant matrices | |
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| Monotone matrices | |
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| Class P | |
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| Tensor Product of Matrices. Compound Matrices | |
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| Tensor product | |
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| Compound matrices | |
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| Matrices and polynomials. Stable Matrices | |
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| Characteristic polynomial | |
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| Matrices associated with polynomials | |
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| Bezout matrices | |
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| Hankel matrices | |
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| Toeplitz and Lowner matrices | |
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| Stable matrices | |
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| Band Matrices | |
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| Band matrices and graphs | |
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| Eigenvalues and eigenvectors of tridiagonal matrices | |
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| Norms and Their Use for Estimation of Eigenvalues | |
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| Norms | |
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| Measure of nonsingularity. Dual norms | |
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| Bounds for eigenvalues | |
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| Direct Methods for Solving Linear Systems | |
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| Nonsingular case | |
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| General case | |
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| Iterative Methods for Solving Linear Systems | |
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| General case | |
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| The Jacobi method | |
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| The Gauss-Seidel method | |
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| The SOR method | |
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| Matrix Inversion | |
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| Inversion of special matrices | |
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| The pseudoinverse | |
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| Numerical Methods for Computing Eigenvalues of Matrices | |
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| Computation of selected eigenvalues | |
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| Computation of all the eigenvalues | |
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| Sparse Matrices | |
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| Storing. Elimination ordering | |
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| Envelopes. Profile | |
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| Bibliography | |
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| Index | |