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Summary of Notation
Matrices
Determinants
Nonsingular matrices Inverse matrices
Schur complement Factorization
Vector spaces Rank
Eigenvectors, eigenvalues Characteristic polynomial
Similarity Jordan normal form
Exercises
Euclidean and unitary spaces
Symmetric and Hermitian matrices
Orthogonal and unitary matrices
GramSchmidt orthonormalization Schur's theorem
Positive definite and positive semidefinite matrices
Sylvester's law of inertia
Singular value decomposition
Exercises
Digraphs
Digraph of a matrix
Undirected graphs Trees
Bigraphs
Exercises
Nonnegative matrices
The PerronFrobenius theorem
Cyclic matrices
Stochastic matrices
Doubly stochastic matrices
Exercises
MMatrices (Matrices of Classes K and Ko)
Class K
Class Ko
Diagonally dominant matrices
Monotone matrices
Class P
Exercises
Tensor Product of Matrices Compound Matrices
Tensor product
Compound matrices
Exercises
Characteristic polynomial
Matrices associated with polynomials
Bezout matrices
Hankel matrices
Toeplitz and Löwner matrices
Stable matrices
Exercises
Band matrices and graphs
Eigenvalues and eigenvectors of tridiagonal matrices
Exercises
Norms
Measure of nonsingularity Dual norms
Bounds for eigenvalues
Exercises
Nonsingular case
General case
Exercises
Iterative Methods for Solving Linear Systems
The Jacobi method
The GaussSeidel method
The SOR method
Exercises
Inversion of special matrices
The pseudo inverse
Exercises
Computation of selected eigenvalues
Computation of all the eigenvalues
Exercises
Storing Elimination ordering
Envelopes Profile
Exercises
Subject Index