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Adventures in the World of Matrices
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CONTENTS Acknowledgements vii Preface xi Presentation 1 Chapter 1 The Concept of a Matrix 3 Chapter 2 Cycles of Numbers 9 Chapter 3 Some Matrices of Alternating Cycles 11 Chapter 4 Alternating Cycle Matrices of Dimensions 4 by 4. First Part 17 Chapter 5 Alternating Cycle Matrices of Dimensions 4 by 4. Second Part 25 Chapter 6 Alternating Cycle Matrices of Dimensions 4 by 4. Third Part: Multiplication Table 31 Chapter 7 More Properties of Alternating Cycle Matrices of Dimensions 4 by 4 39 Chapter 8 Negative Alternating Cycle Matrices of Dimensions 6 by 6 45 Chapter 9 Multiplication of Negative Alternating Cycle Matrices of Dimensions 6 by 6 51 Chapter 10 Multiplication of Positive and Negative Alternating Cycle Matrices of Dimensions 6 by 6 55 Chapter 11 Alternating Cycle Matrices of Even Dimensions 59 Chapter 12 General Hypotheses about Alternating Cycle Matrices of Even Dimensions 67 Chapter 13 Alternating Cycle Matrices of Dimensions 5 by 5 71 Chapter 14 Multiplication of Positive and Negative Alternating Cycle Matrices of Dimensions 3 by 3 77 Chapter 15 Alternating Cycle Matrices of Dimensions 7 by 7 85 x Contents Chapter 16 Multiplication Tables of Basic Positive and Negative Alternating Cycle Matrices of Dimensions 7 by 7 89 Chapter 17 Cyclic Structure of Multiplication Tables 97 Chapter 18 Multiplication Tables of Basic Positive and Negative Alternating Cycle Matrices of Dimensions 6 by 6 101 Chapter 19 Outline of a Proof 107 Chapter 20 Multiplication of Basic Positive Alternating Cycle Matrices of Even Dimensions: Formulation of Hypotheses 111 Chapter 21 Multiplication of Basic Positive Alternating Cycle Matrices of Even Dimensions: Some Proofs 119 Chapter 22 Activities of Proof 125 Chapter 23 Cycle Matrices of Dimensions 6 by 6 and of Period 3 133 Chapter 24 Other Periodic Cycle Matrices of Dimensions 6 by 6 141 Chapter 25 Periodic Cycle Matrices of Odd Dimensions 147 Chapter 26 The World of the Periodic Cycle Matrices 153 Chapter 27 Discover the World of the Cycle Matrices 157 Chapter 28 Cycle Matrices, Genetic Matrices and the Golden Section 161 Chapter 29 Bibliography 165 Chapter 30 Note on the Use of a Computer 167 Appendices 169 Chapter 31 Inverse Matrices 171 Chapter 32 Determinants 175 Chapter 33 Transformations of Alternating Cycle Matrices. Permutations 179 Chapter 34 Polygonal and Circular Representations 185 Index 193 |
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