Adventures in the world of matrices / Paulus Gerdes.

Format:

Book

Author/Creator:

Gerdes, Paulus.

Series:

Contemporary mathematical studies

Language:

English

Subjects (All):

Matrices.

Algebra.

Physical Description:

1 online resource (208 p.)

Edition:

1st ed.

Place of Publication:

New York : Nova Science Publishers, c2007.

Language Note:

English

Summary:

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.

Contents:

Intro

ADVENTURES IN THEWORLD OF MATRICES

NOTICE TO THE READER

ACKNOWLEDGEMENTS

CONTENTS

PREFACE

PRESENTATION

THE CONCEPT OF A MATRIX

ABSTRACT

MULTIPLICATION OF A MATRIX BY A SCALAR

ADDITION OF MATRICES

MULTIPLICATION OF SQUARE MATRICES

ACTIVITIES

IDENTITY MATRIX

HISTORICAL NOTE

NOTATIONS

CYCLES OF NUMBERS

SOME MATRICES OF ALTERNATING CYCLES

ACTIVITY

ALTERNATING CYCLE MATRICES OF DIMENSIONS4 BY 4. FIRST PART

ALTERNATING CYCLE MATRICES OF DIMENSIONS4 BY 4. SECOND PART

Theorem 5.1.

ALTERNATING CYCLE MATRICES OF DIMENSIONS 4BY 4. THIRD PART: MULTIPLICATION TABLE

ANSWERS

MORE PROPERTIES OF ALTERNATING CYCLEMATRICES OF DIMENSIONS 4 BY 4

NEGATIVE ALTERNATING CYCLE MATRICESOF DIMENSIONS 6 BY 6

MULTIPLICATION OF NEGATIVE ALTERNATINGCYCLE MATRICES OF DIMENSIONS 6 BY 6

MULTIPLICATION OF POSITIVE AND NEGATIVEALTERNATING CYCLE MATRICES OFDIMENSIONS 6 BY 6

ALTERNATING CYCLE MATRICESOF EVEN DIMENSIONS

GENERAL HYPOTHESES ABOUT ALTERNATINGCYCLE MATRICES OF EVEN DIMENSIONS

Hypothesis 1a

Hypothesis 1b

Hypothesis 2a

Hypothesis 2b

Hypothesis 3a

Hypothesis 3b

Hypothesis 3c

Hypothesis 4

Hypothesis 5

ALTERNATING CYCLE MATRICESOF DIMENSIONS 5 BY 5.

ABSTRACT

MULTIPLICATION OF POSITIVE AND NEGATIVEALTERNATING CYCLE MATRICES OFDIMENSIONS 3 BY 3

14.1. A Surprising Property of the Multiplication Tables

ALTERNATING CYCLE MATRICESOF DIMENSIONS 7 BY 7

MULTIPLICATION TABLES OF BASIC POSITIVE ANDNEGATIVE ALTERNATING CYCLE MATRICESOF DIMENSIONS 7 BY 7

CYCLIC STRUCTURE OF MULTIPLICATION TABLES

QUESTIONS FOR REFLECTION

MULTIPLICATION TABLES OF BASIC POSITIVE ANDNEGATIVE ALTERNATING CYCLE MATRICESOF DIMENSIONS 6 BY 6

OUTLINE OF A PROOF

MULTIPLICATION OF BASIC POSITIVE ALTERNATINGCYCLE MATRICES OF EVEN DIMENSIONS:FORMULATION OF HYPOTHESES

MULTIPLICATION OF BASIC POSITIVE ALTERNATINGCYCLE MATRICES OF EVEN DIMENSIONS:SOME PROOFS

ACTIVITIES OF PROOF

Theorem 22.1.

Theorem 22.2.

Theorem 22.3.

Theorem 22.4.

Theorem 22.5.

Theorem 22.6.

Theorem 22.7.

Theorem 22.8.

Theorem 22.9.

Theorem 22.10.

Theorem 22.11.

Theorem 22.12.

Theorem 22.13.

CYCLE MATRICES OF DIMENSIONS 6BY 6 AND OF PERIOD 3

OTHER PERIODIC CYCLE MATRICES OFDIMENSIONS 6 BY 6

Theorem 24.1.

PERIOD 4

PERIOD 6

PERIODIC CYCLE MATRICES OF ODD DIMENSIONS

THE WORLD OF THE PERIODIC CYCLE MATRICES.

Theorem 26.1a.

Theorem 26.1b.

Theorem 26.2a.

Theorem 26.3a.

Theorem 26.3b.

Theorem 26.3c.

Theorem 26.4.

Theorem 26.5.

Theorem 26.6.

DISCOVER THE WORLD OF THE CYCLE MATRICES

CYCLE MATRICES, GENETIC MATRICESAND THE GOLDEN SECTION

BIBLIOGRAPHY

CYCLE MATRICES AND LIKI-DESIGNS

HELIX, CYLINDER AND CHESS MATRICES

GENETIC MATRICES (CHAPTER 28)

LUNDA-DESIGNS AND TRADITIONAL DRAWINGS FROM ANGOLA

NOTE ON THE USE OF A COMPUTER

APPENDICES

INVERSE MATRICES

DETERMINANTS

TRANSFORMATIONS OF ALTERNATING CYCLEMATRICES. PERMUTATIONS

POLYGONAL AND CIRCULAR REPRESENTATIONS

INDEX.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-60692-755-8

OCLC:

923658802