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| Title: | Adventures in the World of Matrices
|
| Series: | (Contemporary Mathematical Studies Series) |
| Author: | Paulus Gerdes (ed) |
| ISBN: | 1600217184 : 9781600217180 |
| Illustrations: | tables & charts |
| Format: | Hardback |
| Size: | 180x260mm |
| Pages: | 194 |
| Weight: | .598 Kg. |
| Published: | Nova Science Publishers - April 2007 |
| List Price: | 59.5 Pounds Sterling |
| Availability: | In Print |
| Subjects: | MATHEMATICS |
The purpose of the book is to give the reader a feeling for the beauty and the surprises of mathematical research by building up step by step a theory of cycle matrices. The notions of matrix and cycle are presented for those readers who do not yet know the concepts. Then, starting and experimenting with cycle matrices of low dimensions and engaging the readers in various activities, beautiful results are obtained with attractive geometrical interpretation. Gradually the results are extended to cycle matrices of higher dimensions and then generalised. A note is included for those readers who would like to use a computer in exploring cycle matrices. Two appendices give the possibility to further use the computer by exploring inverses matrices and determinants.
Preface; Presentation; The Concept of Matrix; Cycles of Numbers; Some Matrices of Alternating Cycles; Alternating Cycle Matrices of Dimensions 4 by 4: Part I; Alternating Cycle Matrices of Dimensions 4 by 4: Part II; Alternating Cycle Matrices of Dimensions 4 by 4: : Part III; Some more Properties of Alternating Cycle Matrices of Dimensions 4 by 4; Negative Alternating Cycle Matrices of Dimensions 6 by 6; Multiplication of Negative Alternating Cycle Matrices of Dimensions 6 by 6; Multiplication of Positive and Negative Alternating Cycle Matrices of Dimensions 6 by 6; Alternating Cycle Matrices of Even Dimensions; General Hypotheses Concerning Alternating Cycle Matrices of Even Dimensions; Alternating Cycle Matrices of Dimensions 5 by 5; Multiplication of Positive and Negative Alternating Cycle Matrices of Dimensions 3 by 3; Alternating Cycle Matrices of Dimensions 7 by 7; Multiplication Tables of basic Positive and Negative Alternating Cycle Matrices of Dimensions 7 by 7; Cyclic Structure of the Multiplication Tables; Multiplication Tables of basic Positive and Negative Alternating Cycle Matrices of Dimensions 6 by 6; Outline of a Proof; Multiplication of basic Positive Alternating Cycle Matrices of Even Dimensions: Formulation of Hypotheses; Multiplication of basic Positive Alternating Cycle Matrices of Even Dimensions: Some Proofs; Proof Activities; Cycle Matrices of Dimensions 6 by 6 and of Period 3; Other Periodic Cycle Matrices of Dimensions 6 by 6; Periodic Cycle Matrices of Odd Dimensions; The World of Periodic Cycle Matrices; Discovering the World of Cycle Matrices; Cycle Matrices, Genetic Matrices and the Golden Section; Bibliography; Inverse Matrices; Determinants; Transformations of Alternating Cycle Matrices; Polygonal and Circular Representations; Index.
