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Multidimensional Analysis [electronic resource] : 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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| Format: | Texto biblioteca |
| Language: | eng |
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New York, NY : Springer New York,
1995
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| Subjects: | Mathematics., Applied mathematics., Engineering mathematics., Numerical analysis., Physics., Applications of Mathematics., Physics, general., Numerical Analysis., Appl.Mathematics/Computational Methods of Engineering., |
| Online Access: | http://dx.doi.org/10.1007/978-1-4612-4208-6 |
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KOHA-OAI-TEST:1787852018-07-30T22:58:07ZMultidimensional Analysis [electronic resource] : Algebras and Systems for Science and Engineering / Hart, George W. author. SpringerLink (Online service) textNew York, NY : Springer New York,1995.engThis 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.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.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.Mathematics.Applied mathematics.Engineering mathematics.Numerical analysis.Physics.Mathematics.Applications of Mathematics.Physics, general.Numerical Analysis.Appl.Mathematics/Computational Methods of Engineering.Springer eBookshttp://dx.doi.org/10.1007/978-1-4612-4208-6URN:ISBN:9781461242086 |
| institution |
COLPOS |
| collection |
Koha |
| country |
México |
| countrycode |
MX |
| component |
Bibliográfico |
| access |
En linea En linea |
| databasecode |
cat-colpos |
| tag |
biblioteca |
| region |
America del Norte |
| libraryname |
Departamento de documentación y biblioteca de COLPOS |
| language |
eng |
| topic |
Mathematics. Applied mathematics. Engineering mathematics. Numerical analysis. Physics. Mathematics. Applications of Mathematics. Physics, general. Numerical Analysis. Appl.Mathematics/Computational Methods of Engineering. Mathematics. Applied mathematics. Engineering mathematics. Numerical analysis. Physics. Mathematics. Applications of Mathematics. Physics, general. Numerical Analysis. Appl.Mathematics/Computational Methods of Engineering. |
| spellingShingle |
Mathematics. Applied mathematics. Engineering mathematics. Numerical analysis. Physics. Mathematics. Applications of Mathematics. Physics, general. Numerical Analysis. Appl.Mathematics/Computational Methods of Engineering. Mathematics. Applied mathematics. Engineering mathematics. Numerical analysis. Physics. Mathematics. Applications of Mathematics. Physics, general. Numerical Analysis. Appl.Mathematics/Computational Methods of Engineering. Hart, George W. author. SpringerLink (Online service) Multidimensional Analysis [electronic resource] : Algebras and Systems for Science and Engineering / |
| description |
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. |
| format |
Texto |
| topic_facet |
Mathematics. Applied mathematics. Engineering mathematics. Numerical analysis. Physics. Mathematics. Applications of Mathematics. Physics, general. Numerical Analysis. Appl.Mathematics/Computational Methods of Engineering. |
| author |
Hart, George W. author. SpringerLink (Online service) |
| author_facet |
Hart, George W. author. SpringerLink (Online service) |
| author_sort |
Hart, George W. author. |
| title |
Multidimensional Analysis [electronic resource] : Algebras and Systems for Science and Engineering / |
| title_short |
Multidimensional Analysis [electronic resource] : Algebras and Systems for Science and Engineering / |
| title_full |
Multidimensional Analysis [electronic resource] : Algebras and Systems for Science and Engineering / |
| title_fullStr |
Multidimensional Analysis [electronic resource] : Algebras and Systems for Science and Engineering / |
| title_full_unstemmed |
Multidimensional Analysis [electronic resource] : Algebras and Systems for Science and Engineering / |
| title_sort |
multidimensional analysis [electronic resource] : algebras and systems for science and engineering / |
| publisher |
New York, NY : Springer New York, |
| publishDate |
1995 |
| url |
http://dx.doi.org/10.1007/978-1-4612-4208-6 |
| work_keys_str_mv |
AT hartgeorgewauthor multidimensionalanalysiselectronicresourcealgebrasandsystemsforscienceandengineering AT springerlinkonlineservice multidimensionalanalysiselectronicresourcealgebrasandsystemsforscienceandengineering |
| _version_ |
1756264459316232192 |