Fundamentals of linear algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton
CRC Press, Taylor & Francis Group
2019
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| Series: | Textbooks in mathematics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xii,227 Seiten |
| ISBN: | 9781138590502 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents Preface ix Advice to the Reader xi 1 Preliminaries 1.1 What Is Linear Algebra? ........................................................... 1.2 Rudimentary Set Theory .................................................. ... . 1.3 Cartesian Products .................................................................. 1.4 Relations .................................................................... 1.5 Concept of a Function............................................................... 1.6 Composite Functions .............................................................. 1.7 Fields of Scalars ........................................................................ 1.8 Techniques for Proving Theorems .......................................... 1 1 2 3 4 4 7 8 11 2 Matrix Algebra 2.1 Matrix Operations.................................................. 2.1.1 Addition and Scaling of Matrices:...................... 2.1.2 Matrix Multiplication...................................... 2.2 Geometric Meaning of a Matrix Equation .............................. 2.3 Systems of Linear Equations ................................................... 2.4 Inverse of a Matrix ............... .. ........................ ;. ..... . 2.5 The Equation Ax = b ............................................................... 2.6 Basic Applications................. 2.6.1 Traffic Flow.......................... 2.6.2 Barter Systems.................... 2.6.3 Electric Circuits............................................... 2.6.4 Chemical Reactions . ................................... 2.6.5
Economics..................... . . . ..................... ................. 17 17 18 19 25 27 33 38 39 39 40 42 43 44 3 Vector Spaces 3.1 The Concept of a Vector Space................................................ 3.2 Subspaces........................................................... 3.3 The Dimension of a Vector Space .............................. 3.4 Linear Independence........................................................... 3.5 Application of Knowing dim(V) .......................................... . 3.6 Coordinates .............................................................. 3.7 Rank of a Matrix .............................................................. 47 47 52 56 58 63 65 68 v
vi Contents 4 Linear Maps 4.1 Linear Maps ............................................................................. 4.2 Properties of Linear Maps ...................................................... 4.3 Matrix of a Linear Map............................................................ 4.4 Matrix Algebra and Algebra of Linear Maps ........................ 4.5 Linear Functionals and Duality................................................ 4.6 Equivalence and Similarity ...................................................... 4.7 Application to Higher Order Differential Equations ............ 71 71 76 80 84 87 88 90 5 Determinants 5.1 Motivation ................................................................................ 5.2 Properties of Determinants...................................................... 5.3 Existence and Uniqueness of Determinant.............................. 5.4 Computational Definition of Determinant.............................. 5.5 Evaluation of Determinants...................................................... 5.6 Adjoint and Cramer’s Rule...................................................... 93 93 96 97 102 105 108 6 Diagonalization 6.1 Motivation ................................................................................ 6.2 Eigenvalues and Eigenvectors................................................... 6.3 Cayley-Hamilton Theorem ...................................................... 113 113 114 123 7 Inner Product Spaces 7.1 Inner Product .......................................................................... 7.2 Fourier
Series............................................................................. 7.3 Orthogonal and Orthonormal Sets.......................................... 7.4 Gram-Schmidt Process ............................................................ 7.5 Orthogonal Projections on Subspaces .................................... 127 127 133 134 136 140 8 Linear Algebra over Complex Numbers 8.1 Algebra of Complex Numbers ................................................ 8.2 Diagonalization of Matrices with Complex Eigenvalues . . . 8.3 Matrices over Complex Numbers............................................. 147 147 150 151 9 Orthonormal Diagonalization 9.1 Motivational Introduction......................................................... 9.2 Matrix Representation of a Quadratic Form ........................ 9.3 Spectral Decomposition............................................................ 9.4 Constrained Optimization - Extrema of Spectrum............... 9.5 Singular Value Decomposition (SVD) .................................... 157 157 159 161 167 168 10 Selected Applications of Linear Algebra 10.1 System of First Order Linear Differential Equations ............ 10.2 Multivariable Calculus ............................................................ 10.3 Special Theory of Relativity ................................................... 10.4 Cryptography ........................................................................... 177 177 179 181 190
Contents 10.5 Solving Famous Problems from Greek Geometry................... 10.5.1 Vector Spaces of Polynomials........................................ 10.5.2 Roots of Polynomials........................................................ 10.5.3 Straightedge and Compass . ............................................ 10.5.4 Intersecting Lines and Circles........................................ 10.5.5 Degrees of Constructible Numbers............................... 10.5.6 Solutions of the Famous Problems............................... vii 196 196 198 201 203 204 204 Answers to Selected Numerical Problems 207 Notation 219 Bibliography 221 Index 223
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| spelling | Chahal, J. S. aut Fundamentals of linear algebra J.S. Chahal Boca Raton CRC Press, Taylor & Francis Group 2019 xii,227 Seiten txt rdacontent n rdamedia nc rdacarrier Textbooks in mathematics Includes bibliographical references and index Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content (DE-588)4123623-3 Lehrbuch gnd-content Lineare Algebra (DE-588)4035811-2 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031480695&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Fundamentals of linear algebra |
| title_auth | Fundamentals of linear algebra |
| title_exact_search | Fundamentals of linear algebra |
| title_full | Fundamentals of linear algebra J.S. Chahal |
| title_fullStr | Fundamentals of linear algebra J.S. Chahal |
| title_full_unstemmed | Fundamentals of linear algebra J.S. Chahal |
| title_short | Fundamentals of linear algebra |
| title_sort | fundamentals of linear algebra |
| topic | Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algebras, Linear Textbooks Lineare Algebra Einführung Lehrbuch |
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