Preface / I: |
Basic Theory / 1: |
Geršgorin's Theorem / 1.1: |
Extensions of Geršgorin's Theorem via Graph Theory / 1.2: |
Analysis Extensions of Geršgorin's Theorem and Fan's Theorem / 1.3: |
A Norm Derivation of Geršgorin's Theorem 1.1 / 1.4: |
Geršgorin-Type Eigenvalue Inclusion Theorems / 2: |
Brauer's Ovals of Cassini / 2.1: |
Higher-Order Lemniscates / 2.2: |
Comparison of the Brauer Sets and the Brualdi Sets / 2.3: |
The Sharpness of Brualdi Lemniscate Sets / 2.4: |
An Example / 2.5: |
More Eigenvalue Inclusion Results / 3: |
The Parodi-Schneider Eigenvalue Inclusion Sets / 3.1: |
The Field of Values of a Matrix / 3.2: |
Newer Eigenvalue Inclusion Sets / 3.3: |
The Pupkov-Solov'ev Eigenvalue Inclusions Set / 3.4: |
Minimal Geršgorin Sets and Their Sharpness / 4: |
Minimal Geršgorin Sets / 4.1: |
Minimal Geršgorin Sets via Permutations / 4.2: |
A Comparison of Minimal Geršgorin Sets and Brualdi Sets / 4.3: |
G-Functions / 5: |
The Sets <$>{\cal F}_{\bf n}<$> and <$>{\cal G}_{\bf n}<$> / 5.1: |
Structural Properties of <$>{\cal G}_{\bf n}<$> and <$>{\cal G}_{\bf n}^{\bf c}<$> / 5.2: |
Minimal G-Functions / 5.3: |
Minimal G-Functions with Small Domains of Dependence / 5.4: |
Connections with Brauer Sets and Generalized Brualdi Sets / 5.5: |
Geršgorin-Type Theorems for Partitioned Matrices / 6: |
Partitioned Matrices and Block Diagonal Dominance / 6.1: |
A Different Norm Approach / 6.2: |
A Variation on a Theme by Brualdi / 6.3: |
G-Functions in the Partitioned Case / 6.4: |
Geršgorin's Paper from 1931, and Comments / Appendix A: |
Vector Norms and Induced Operator Norms / Appendix B: |
The Perron-Frobenius Theory of Nonnegative Matrices / Appendix C: |
Matlab 6 Programs / Appendix D: |
References |
Preface / I: |
Basic Theory / 1: |
Geršgorin's Theorem / 1.1: |
Extensions of Geršgorin's Theorem via Graph Theory / 1.2: |
Analysis Extensions of Geršgorin's Theorem and Fan's Theorem / 1.3: |
A Norm Derivation of Geršgorin's Theorem 1.1 / 1.4: |