Multidimensional Analysis: Algebras and Systems for Science and Engineering [Hardcover]

George W. Hart (Author)

Book Description

ISBN-10: 0387944176 | ISBN-13: 978-0387944173 | Publication Date: December 7, 1995 | Edition: 1

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.

Editorial Reviews

Review

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.”

Product Details

• Hardcover: 236 pages
• Publisher: Springer; 1 edition (December 7, 1995)
• Language: English
• ISBN-10: 0387944176
• ISBN-13: 978-0387944173
• Product Dimensions: 9.3 x 6.1 x 0.8 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,989,585 in Books (See Top 100 in Books)

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2 of 2 people found the following review helpful:

4.0 out of 5 stars Intersting perspective on an underapreciated topic, July 26, 2009

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Eassin - See all my reviews

This review is from: Multidimensional Analysis: Algebras and Systems for Science and Engineering (Hardcover)

Interesting book, but it could have used a bit more fleshing out.

Chapters 0, and 8 discuss dimensions of measurement and why keeping track of units is important.

Chapter 1 makes assumption that dimensional measurements form a mathematical group and discusses some properties he thinks the group should have. I was hoping for a full explication on the groups that could work here, but was directed to the referencs.

Chapters 2, 3, and 4 derive a consistent linear algebra with his group elements as entries. The assumptions in chapter 1 could be done away with if he added a couple of words about how linear algebra would work over any group.

Chapter 7 should come after chapter 4. It discussed how traditional dimensional analysis problems like the pendulum might scale up to matrix operations. He shoots himself in the foot by saying that the Hadamard product is irrelevant to multidimensional analysis, when the dimensional inverse that he defines in chapter 2 and then uses on nearly every page is the transpose of the Hadamard inverse. Developing that observation could have been very insightful.

Chapeter 5 discusses the primary application as systems theory. Some better groundwork of the basics of system theory and some examples of setting dimensioned problems up as systems would have been appreciated.

Chapter 6 is about how to program the neccesary mathematics into a computer circa 1995. It should have been in an appendix or dropped altogether.