Ebook: Multidimensional Analysis: Algebras and Systems for Science and Engineering

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.

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Content:
Front Matter....Pages i-xi
Introductory....Pages 1-15
The Mathematical Foundations of Science and Engineering....Pages 17-55
Dimensioned Linear Algebra....Pages 57-84
The Theory of Dimensioned Matrices....Pages 85-118
Norms, Adjoints, and Singular Value Decomposition....Pages 119-144
Aspects of the Theory of Systems....Pages 145-170
Multidimensional Computational Methods....Pages 171-208
Forms of Multidimensional Relationships....Pages 209-217
Concluding Remarks....Pages 219-221
Solutions to Odd-Numbered Exercises....Pages 223-226
Back Matter....Pages 227-236

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Content:
Front Matter....Pages i-xi
Introductory....Pages 1-15
The Mathematical Foundations of Science and Engineering....Pages 17-55
Dimensioned Linear Algebra....Pages 57-84
The Theory of Dimensioned Matrices....Pages 85-118
Norms, Adjoints, and Singular Value Decomposition....Pages 119-144
Aspects of the Theory of Systems....Pages 145-170
Multidimensional Computational Methods....Pages 171-208
Forms of Multidimensional Relationships....Pages 209-217
Concluding Remarks....Pages 219-221
Solutions to Odd-Numbered Exercises....Pages 223-226
Back Matter....Pages 227-236
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