Multidimensional analysis: algebras and systems for science and engineering
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1995
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 236 S. graph. Darst. |
| ISBN: | 0387944176 |
Internformat
MARC
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| 100 | 1 | |a Hart, George W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Multidimensional analysis |b algebras and systems for science and engineering |c George W. Hart |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1995 | |
| 300 | |a X, 236 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Analyse multivariée |2 ram | |
| 650 | 7 | |a Modèles mathématiques |2 ram | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Dimensional analysis | |
| 650 | 4 | |a Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1804124572735242240 |
|---|---|
| adam_text | Contents
0. Introductory 1
0.1 Physical Dimensions 2
0.2 Mathematical Dimensions 6
0.3 Overview 12
Exercises 14
1. The Mathematical Foundations of Science
and Engineering 17
1.1 The Inadequacy of Real Numbers 19
1.1.1 The Error of Substitution 20
1.1.2 The Problem with Linear Spaces 22
1.1.3 Nondimensionalization 24
1.1.3 Dimensioned Algebras 25
1.2 The Mathematics of Dimensioned Quantities 27
1.2.1 Axiomatic Development 29
1.2.2 Constructive Approach 32
1.2.3 Constraints on Exponentiation 34
1.2.4 The Dimensional Basis 36
1.2.5 Dimensional Logarithms 40
1.2.6 The Basis Independence Principle 42
1.2.7 Symmetries of Dimensioned Quantities 45
1.2.8 Images 48
1.3 Conclusions 53
Exercises 54
2. Dimensioned Linear Algebra 57
2.1 Vector Spaces and Linear Transformations 59
2.2 Terminology and Dimensional Inversion 63
2.3 Dimensioned Scalars 68
2.4 Dimensioned Vectors 72
viii Contents
2.5 Dimensioned Matrices 77
Exercises 84
3. The Theory of Dimensioned Matrices 85
3.1 The Dimensional Freedom of Multipliable Matrices 85
3.2 Endomorphic Matrices and the Matrix Exponential 87
3.3 Square Matrices, Inverses, and the Determinant 92
3.4 Squarable Matrices and Eigenstructure 96
3.5 Dimensionally Symmetric Multipliable Matrices 99
3.6 Dimensionally Hankel and Toeplitz Matrices 103
3.7 Uniform, Half Uniform, and Dimensionless Matrices 105
3.8 Conclusions 109
3.A Appendix: The n + m 1 Theorem 112
Exercises 117
4. Norms, Adjoints, and Singular Value
Decomposition 119
4.1 Norms for Dimensioned Spaces 121
4.1.1 Wand Norms 121
4.1.2 Extrinsic Norms 122
4.2 Dimensioned Singular Value Decomposition (DSVD) 124
4.3 Adjoints 132
4.4 Norms for Nommiform Matrices 134
4.5 A Control Application 137
4.6 Factorization of Symmetric Matrices 139
Exercises 144
5. Aspects of the Theory of Systems 145
5.1 Differential and Difference Equations 146
5.2 State Space Forms 149
5.3 Canonical Forms 151
5.4 Transfer Functions and Impulse Responses 159
5.5 Duals and Adjoints 161
5.6 Stability 162
5.7 Controllability, Observability, and Grammians 163
5.8 Expectations and Probability Densities 167
Exercises 169
6. Multidimensional Computational Methods 171
6.1 Computers and Engineering 171
6.1.1 A Software Environment for Dimensioned Linear Algebra 172
6.1.2 Overview 173
6.2 Representing and Manipulating Dimensioned Scalars 174
6.2.1 The Numeric and Dimensional Components of a Scalar 174
Contents ix
6.2.2 The Dimensional Basis 175
6.2.3 Numerical Representations and Uniqueness 176
6.2.4 Scalar Operations 177
6.2.5 Input String Conversion 180
6.2.6 Output and Units Conversion 181
6.2.7 Binary Relations 183
6.2.8 Summary of Scalar Methods 184
6.3 Dimensioned Vectors 185
6.3.1 Dimensioned Vectors and Dimension Vectors 185
6.3.2 Representing Dimensioned Vectors 186
6.3.3 Vector Operations 188
6.3.4 Summary of Vectors 190
6.4 Representing Dimensioned Matrices 190
6.4.1 Arrays versus Matrices 190
6.4.2 The Domain/Range Matrix Representation 191
6.4.3 Allowing Geometric and Matrix Algebra Interpretations 193
6.4.4 Input Conversion 196
6.4.5 Output Conversion 198
6.4.6 Special Classes of Dimensioned Matrices 198
6.4.7 Identity and Zero Matrices 199
6.4.8 Scalar and Vector Conversion to Matrices 200
6.4.9 Summary of the Matrix Representation 201
6.5 Operations on Dimensioned Matrices 201
6.5.1 Matrix Addition, Subtraction, Similarity, and Equality 201
6.5.2 Block Matrices 202
6.5.3 Matrix Multiplication 203
6.5.4 Gaussian Elimination 204
6.5.5 The Determinant and Singularity 204
6.5.6 The Trace 205
6.5.7 Matrix Inverse 205
6.5.8 Matrix Transpose 205
6.5.9 Eigenstructure Decomposition 205
6.5.10 Singular Value Decomposition 206
6.6 Conclusions 206
Exercises 208
7. Forms of Multidimensional Relationships 209
7.1 Goals 209
7.2 Operations 212
7.3 Procedure 214
Exercises 217
8. Concluding Remarks 219
x Contents
9. Solutions to Odd Numbered Exercises 223
References 227
Index 231
|
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| discipline | Physik Technik Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:47:48Z |
| institution | BVB |
| isbn | 0387944176 |
| language | English |
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| physical | X, 236 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| spelling | Hart, George W. Verfasser aut Multidimensional analysis algebras and systems for science and engineering George W. Hart New York [u.a.] Springer 1995 X, 236 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse multivariée ram Modèles mathématiques ram Mathematisches Modell Dimensional analysis Mathematical models Dimensionsanalyse (DE-588)4133116-3 gnd rswk-swf Dimensionsanalyse (DE-588)4133116-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006758364&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hart, George W. Multidimensional analysis algebras and systems for science and engineering Analyse multivariée ram Modèles mathématiques ram Mathematisches Modell Dimensional analysis Mathematical models Dimensionsanalyse (DE-588)4133116-3 gnd |
| subject_GND | (DE-588)4133116-3 |
| title | Multidimensional analysis algebras and systems for science and engineering |
| title_auth | Multidimensional analysis algebras and systems for science and engineering |
| title_exact_search | Multidimensional analysis algebras and systems for science and engineering |
| title_full | Multidimensional analysis algebras and systems for science and engineering George W. Hart |
| title_fullStr | Multidimensional analysis algebras and systems for science and engineering George W. Hart |
| title_full_unstemmed | Multidimensional analysis algebras and systems for science and engineering George W. Hart |
| title_short | Multidimensional analysis |
| title_sort | multidimensional analysis algebras and systems for science and engineering |
| title_sub | algebras and systems for science and engineering |
| topic | Analyse multivariée ram Modèles mathématiques ram Mathematisches Modell Dimensional analysis Mathematical models Dimensionsanalyse (DE-588)4133116-3 gnd |
| topic_facet | Analyse multivariée Modèles mathématiques Mathematisches Modell Dimensional analysis Mathematical models Dimensionsanalyse |
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