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Multidimensional Analysis : Algebras and Systems for Science and Engineering

Author: George W Hart
Publisher: New York, NY : Springer New York, 1995.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: George W Hart
ISBN: 9781461242086 1461242088
OCLC Number: 852793228
Description: 1 online resource (xi, 236 pages 19 illustrations)
Contents: 0. Introductory --
0.1 Physical Dimensions --
0.2 Mathematical Dimensions --
0.3 Overview --
Exercises --
1. The Mathematical Foundations of Science and Engineering --
1.1 The Inadequacy of Real Numbers --
1.2 The Mathematics of Dimensioned Quantities --
1.3 Conclusions --
Exercises --
2. Dimensioned Linear Algebra --
2.1 Vector Spaces and Linear Transformations --
2.2 Terminology and Dimensional Inversion --
2.3 Dimensioned Scalars --
2.4 Dimensioned Vectors --
2.5 Dimensioned Matrices --
Exercises --
3. The Theory of Dimensioned Matrices --
3.1 The Dimensional Freedom of Multipliable Matrices --
3.2 Endomorphic Matrices and the Matrix Exponential --
3.3 Square Matrices, Inverses, and the Determinant --
3.4 Squarable Matrices and Eigenstructure --
3.5 Dimensionally Symmetric Multipliable Matrices --
3.6 Dimensionally Hankel and Toeplitz Matrices --
3.7 Uniform, Half Uniform, and Dimensionless Matrices --
3.8 Conclusions --
3.A Appendix: The n + m? 1 Theorem --
Exercises --
4. Norms, Adjoints, and Singular Value Decomposition --
4.1 Norms for Dimensioned Spaces --
4.2 Dimensioned Singular Value Decomposition (DSVD) --
4.3 Adjoints --
4.4 Norms for Nonuniform Matrices --
4.5 A Control Application --
4.6 Factorization of Symmetric Matrices --
Exercises --
5. Aspects of the Theory of Systems --
5.1 Differential and Difference Equations --
5.2 State-Space Forms --
5.3 Canonical Forms --
5.4 Transfer Functions and Impulse Responses --
5.5 Duals and Adjoints --
5.6 Stability --
5.7 Controllability, Observability, and Grammians --
5.8 Expectations and Probability Densities --
Exercises --
6. Multidimensional Computational Methods --
6.1 Computers and Engineering --
6.2 Representing and Manipulating Dimensioned Scalars --
6.3 Dimensioned Vectors --
6.4 Representing Dimensioned Matrices --
6.5 Operations on Dimensioned Matrices --
6.6 Conclusions --
Exercises --
7. Forms of Multidimensional Relationships --
7.1 Goals --
7.2 Operations --
7.3 Procedure --
Exercises --
8. Concluding Remarks --
9. Solutions to Odd-Numbered Exercises --
References.
Responsibility: by George W. Hart.

Abstract:

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  Read more...

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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 Read more...

 
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