Subject Code: MA7L002 Subject Name: Non-Negative Matrix Theory L-T-P: 4-0-0 Credit:4
Pre-requisite(s): Linear Algebra ( MA5L001)
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.
Text Books:
  1. Berman and Plemmons. Nonnegative Matrices in the Mathematical Sciences, SIAM
  2. Minc H. Nonnegative matrices, Wiley-Interscience Pub.
Reference Books:
  1. Bapat and Raghavan, Nonnegative Matrices and Applications, Cambridge University Press
  2. Horn R. A. and Johnson C. R.  Matrix Analysis, Cambridge University Press
  3. Seneta E., Non-negative Matrices and Markov Chains, Springer