SMARANDACHE LINEAR ALGEBRA Vasantha-Book10

SMARANDACHE LINEAR ALGEBRA Vasantha-Book10 - w. b. vasantha...

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w. b. vasantha kandasamy LINEAR ALGEBRA AND SMARANDACHE LINEAR ALGEBRA AMERICAN RESEARCH PRESS 2003
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1 Linear Algebra and Smarandache Linear Algebra W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036, India American Research Press 2003
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2 This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 N. Zeeb Road P.O. Box 1346, Ann Arbor MI 48106-1346, USA Tel.: 1-800-521-0600 (Customer Service) http://wwwlib.umi.com/bod/ and online from: Publishing Online, Co. (Seattle, Washington State) at: http://PublishingOnline.com This book has been peer reviewed and recommended for publication by: Jean Dezert, Office National d = Etudes et de Recherches Aerospatiales (ONERA), 29, Avenue de la Division Leclerc, 92320 Chantillon, France. M. Khoshnevisan, School of Accounting and Finance, Griffith University, Gold Coast, Queensland 9726, Australia. Sabin Tabirca and Tatiana Tabirca, University College Cork, Cork, Ireland. Copyright 2003 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books can be downloaded from our E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN : 1-931233-75-6 Standard Address Number : 297-5092 Printed in the United States of America
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3 CONTENTS PREFACE 5 Chapter One LINEAR ALGEBRA : Theory and Applications 1.1 Definition of linear Algebra and its properties 7 1.2 Linear transformations and linear operators 12 1.3 Elementary canonical forms 20 1.4 Inner product spaces 29 1.5 Operators on inner product space 33 1.6 Vector spaces over finite fields Z p 37 1.7 Bilinear forms and its properties 44 1.8 Representation of finite groups 46 1.9 Semivector spaces and semilinear algebra 48 1.10 Some applications of linear algebra 60 Chapter Two SMARANDACHE LINEAR ALGEBRA AND ITS PROPERTIES 2.1 Definition of different types of Smarandache linear algebra with examples 65 2.2 Smarandache basis and S-linear transformation of S-vector spaces 71 2.3 Smarandache canonical forms 76 2.4 Smarandache vector spaces defined over finite S-rings Z n 81 2.5 Smarandache bilinear forms and its properties 86 2.6 Smarandache representation of finite S-semigroup 88 2.7 Smarandache special vector spaces 99 2.8 Algebra of S-linear operators 103 2.9 Miscellaneous properties in Smarandache linear algebra 110 2.10 Smarandache semivector spaces and Smarandache semilinear algebras 119
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4 Chapter Three SMARANDACHE LINEAR ALGEBRAS AND ITS APPLICATIONS 3.1 A smattering of neutrosophic logic using S-vector spaces of type II 141 3.2 Smarandache Markov Chains using S-vector spaces II 142 3.3 Smarandache Leontief economic models 143 3.4 Smarandache anti-linear algebra 146 Chapter Four SUGGESTED PROBLEMS 149 REFERENCES 165 INDEX 169
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5 PREFACE While I began researching for this book on linear algebra, I was a little startled.
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SMARANDACHE LINEAR ALGEBRA Vasantha-Book10 - w. b. vasantha...

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