viii CONTENTS Bibliography 66 Chapter 8. Tournaments 67 8.1. Landau’s Theorem 67 8.2. A Special Tournament in T (R) 71 8.3. Eigenvalues of Tournament Matrices 74 Bibliography 76 Chapter 9. Two Matrix Polytopes 77 9.1. The Doubly Stochastic Polytope 77 9.2. Alternating Sign Matrices 79 9.3. The Alternating Sign Matrix Polytope 81 9.4. ASM Patterns 83 Bibliography 86 Chapter 10. Digraphs and Eigenvalues of (0, 1)-matrices 87 10.1. (0, 1)-matrices with all Eigenvalues Positive 87 10.2. Totally Nonnegative Matrices 90 10.3. Totally Nonnegative (0, 1)-matrices 91 Bibliography 93 Index 95
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