Ebook: Matrix Norms and their Applications

1 — Operators in Finite-Dimensional Normed Spaces.- §1. Norms of vectors, linear functionals, and linear operators.- §2. Survey of spectral theory.- §3. Spectral radius.- §4. One-parameter groups and semigroups of operators.- Appendix. Conditioning in general computational problems.- 2 — Spectral Properties of Contractions.- §1. Contractive operators and isometries.- §2. Stability theorems.- §3. One-parameter semigroups of contractions and groups of isometries.- §4. The boundary spectrum of extremal contractions.- §5. Extreme points of the unit ball in the space of operators.- §6. Critical exponents.- §7. The apparatus of functions on graphs.- §8. Combinatorial and spectral properties of l?-contractions.- §9. Combinatorial and spectral properties of nonnegative matrices.- §10. Finite Markov chains.- §11. Nonnegative projectors.- 3 — Operator Norms.- §1. Ring norms on the algebra of operators in E.- §2. Characterization of operator norms.- §3. Operator minorants.- §4. Suprema of families of operator norms.- §5. Ring cross-norms.- §6. Orthogonally-invariant norms.- 4 — Study of the Order Structure on the Set of Ring Norms.- §1. Maximal chains of ring norms.- §2. Generalized ring norms.- §3. The lattice of subalgebras of the algebra End(E).- §4. Characterization of automorphisms.- Brief Comments on the Literature.- References.