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© 1995

Multidimensional Analysis

Algebras and Systems for Science and Engineering

Textbook

Table of contents

  1. Front Matter
    Pages i-xi
  2. George W. Hart
    Pages 1-15
  3. George W. Hart
    Pages 57-84
  4. George W. Hart
    Pages 85-118
  5. George W. Hart
    Pages 145-170
  6. George W. Hart
    Pages 171-208
  7. George W. Hart
    Pages 209-217
  8. George W. Hart
    Pages 219-221
  9. George W. Hart
    Pages 223-226
  10. Back Matter
    Pages 227-236

About this book

Introduction

This book deals with the mathematical properties of dimensioned quantities, such as length, mass, voltage, and viscosity.
Beginning with a careful examination of how one expresses the numerical results of a measurement and uses these results in subsequent manipulations, the author rigorously constructs the notion of dimensioned numbers and discusses their algebraic structure. The result is a unification of linear algebra and traditional dimensional analysis that can be extended from the scalars to which the traditional analysis is perforce restricted to multidimensional vectors of the sort frequently encountered in engineering, systems theory, economics, and other applications.

Keywords

Algebra Analysis calculus linear algebra stability systems theory transformation

Authors and affiliations

  1. 1.Department of Electrical EngineeringColumbia UniversityNew YorkUSA

Bibliographic information

Reviews

FROM THE REVIEWS:

ZENTRALBLATT MATH
"As the book is addressed to physicists, engineers, economists and scientists in a broad sense, who are using linear algebra and linear systems theory in the multidimensional setting, the potential reader will find here a consistent and clear exposition of basic ideas and applications which meet their needs. To the more mathematically minded readers the book offers interesting structures and concepts that deserve generalization.”