Non-Negative Matrix Theory

Matrices which leave a cone invariant: Introduction, Cones, Convex cones, Polyhedral cones, Solids, Spectral properties of matrices which leave a cone invariant, Cone primitivity. Nonnegative Matrices: Nonnegative matrices , Inequalities and Generalities, Positive matrices, Nonnegative Irriducible Matrices, Perron’s Theorem, Perron-Frobenius Theory, Nonsingular M-matrices. Reducible Matrices, Primitive Matrices, A Genenral Limit Theorem Stochastic and Doubly Stochastic Matrices: The Birkhoff-von Neumann Theorem, Fully indecomposable matrices, Konig's Theorem and rank. Semigroups of Nonnegative Matrices: Algebraic semigroups, Nonnegative idempotents, The semigroup Nn, The semigroup Doubly Stochastic Matrices Dn. Symmetric Nonnegative Matrices: Inverse eigenvalue problems, Nonnegative matrices with given sums, Some applications.