Verfügbarkeit: Linear algebra

Linear algebra: a course for physicists and engineers

Gespeichert in:

Bibliographische Detailangaben
Hauptverfasser:	Mathai, Arakaparampil M. 1935- (VerfasserIn), Haubold, Hans J. 1951- (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Berlin ; Boston De Gruyter [2017]
Schriftenreihe:	De Gruyter Textbook
Schlagworte:	Lineare Algebra Eigenvektor Matrix
Online-Zugang:	Volltext Volltext Volltext Inhaltsverzeichnis
Beschreibung:	Erscheint als Open Access bei De Gruyter
Beschreibung:	1 Online-Ressource
ISBN:	9783110562507 9783110562590
DOI:	10.1515/9783110562507

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Datensatz im Suchindex

DE-BY-FWS_katkey	661111
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adam_text	CONTENTS PREFACE * IX ACKNOWLEDGEMENT * XI LIST OF SYMBOLS * XVII 1 VECTORS * 1 1.0 INTRODUCTION * 1 1.1 VECTORS AS ORDERED SETS * 1 1.2 GEOMETRY OF VECTORS * 14 1.2.1 GEOMETRY OF SCALAR MULTIPLICATION * 14 1.2.2 GEOMETRY OF ADDITION OF VECTORS * 14 1.2.3 A COORDINATE-FREE DEFINITION OF VECTORS * 15 1.2.4 GEOMETRY OF DOT PRODUCTS * 16 1.2.5 CAUCHY-SCHWARTZ INEQUALITY * 17 1.2.6 ORTHOGONAL AND ORTHONORMAL VECTORS * 19 1.2.7 PROJECTIONS * 21 1.2.8 WORK DONE * 24 1.3 LINEAR DEPENDENCE AND LINEAR INDEPENDENCE OF VECTORS * 28 1.3.1 A VECTOR SUBSPACE ----- 38 1.3.2 GRAM-SCHMIDT ORTHOGONALIZATION PROCESS * 42 1.4 SOME APPLICATIONS * 48 1.4.1 PARTIAL DIFFERENTIAL OPERATORS * 48 1.4.2 MAXIMA/MINIMA OF A SCALAR FUNCTION OF MANY REAL SCALAR VARIABLES 1.4.3 DERIVATIVES OF LINEAR AND QUADRATIC FORMS * 50 1.4.4 MODEL BUILDING ----- 52 2 MATRICES * 59 2.0 INTRODUCTION * 59 2.1 VARIOUS DEFINITIONS * 60 2.1.1 SOME MORE PRACTICAL SITUATIONS * 75 2.2 MORE PROPERTIES OF MATRICES * 81 2.2.1 SOME MORE PRACTICAL SITUATIONS * 87 2.2.2 PRE AND POST MULTIPLICATIONS BY DIAGONAL MATRICES * 95 2.3 ELEMENTARY MATRICES AND ELEMENTARY OPERATIONS * 100 2.3.1 PREMULTIPLICATION OF A MATRIX BY ELEMENTARY MATRICES * 102 2.3.2 REDUCTION OF A SQUARE MATRIX INTO A DIAGONAL FORM * 111 2.3.3 SOLVING A SYSTEM OF LINEAR EQUATIONS * 113 2.4 INVERSE, LINEAR INDEPENDENCE AND RANKS ----- 121 2.4.1 INVERSE OF A MATRIX BY ELEMENTARY OPERATIONS * 121 2.4.2 CHECKING LINEAR INDEPENDENCE THROUGH ELEMENTARY OPERATIONS * 124 2.5 ROW AND COLUMN SUBSPACES AND NULL SPACES ----- 128 2.5.1 THE ROW AND COLUMN SUBSPACES ----- 129 2.5.2 CONSISTENCY OF A SYSTEM OF LINEAR EQUATIONS * 133 2.6 PERMUTATIONS AND ELEMENTARY OPERATIONS ON THE RIGHT * 138 2.6.1 PERMUTATIONS * 138 2.6.2 POSTMULTIPLICATIONS BY ELEMENTARY MATRICES * 138 2.6.3 REDUCTION OF QUADRATIC FORMS TO THEIR CANONICAL FORMS * 145 2.6.4 ROTATIONS ----- 147 2.6.5 LINEAR TRANSFORMATIONS * 148 2.6.6 ORTHOGONAL BASES FOR A VECTOR SUBSPACE * 152 2.6.7 A VECTOR SUBSPACE, A MORE GENERAL DEFINITION * 154 2.6.8 A LINEAR TRANSFORMATION, A MORE GENERAL DEFINITION * 156 2.7 PARTITIONING OF MATRICES * 160 2.7.1 PARTITIONING AND PRODUCTS ----- 161 2.7.2 PARTITIONING OF QUADRATIC FORMS * 164 2.7.3 PARTITIONING OF BILINEAR FORMS * 165 2.7.4 INVERSES OF PARTITIONED MATRICES * 166 2.7.5 REGRESSION ANALYSIS ----- 170 2.7.6 DESIGN OF EXPERIMENTS * 172 3 DETERMINANTS * 181 3.0 INTRODUCTION ----- 181 3.1 DEFINITION OF THE DETERMINANT OF A SQUARE MATRIX * 181 3.1.1 SOME GENERAL PROPERTIES * 183 3.1.2 A MECHANICAL WAY OF EVALUATING A 3 X 3 DETERMINANT * 189 3.1.3 DIAGONAL AND TRIANGULAR BLOCK MATRICES ----- 195 3.2 COFACTOR EXPANSIONS * 203 3.2.1 COFACTORS AND MINORS * 203 3.2.2 INVERSE OF A MATRIX IN TERMS OF THE COFACTOR MATRIX * 208 3.2.3 A MATRIX DIFFERENTIAL OPERATOR * 211 3.2.4 PRODUCTS AND SQUARE ROOTS * 215 3.2.5 CRAMERS RULE FOR SOLVING SYSTEMS OF LINEAR EQUATIONS 216 3.3 SOME PRACTICAL SITUATIONS ------ 223 3.3.1 CROSS PRODUCT ----- 223 3.3.2 AREAS AND VOLUMES ----- 225 3.3.3 JACOBIANS OF TRANSFORMATIONS * 229 3.3.4 FUNCTIONS OF MATRIX ARGUMENT * 239 3.3.5 PARTITIONED DETERMINANTS AND MULTIPLE CORRELATION COEFFICIENT ----- 241 3.3.6 MAXIMA/MINIMA PROBLEMS * 245 4 4.0 4.1 4.2 4.2.1 4.2.2 4.2.3 4.3 4.3.1 4.3.2 4.3.3 4.3.4 4.3.5 4.3.6 4.4 4.4.1 4.4.2 4.4.3 5 5.0 5.1 5.1.1 5.1.2 5.1.3 5.2 5.2.1 5.2.2 5.3 5.3.1 5.3.2 5.3.3 5.3.4 5.4 5.4.1 5.4.2 5.5 5.5.1 5.5.2 EIGENVALUES AND EIGENVECTORS * 253 INTRODUCTION ----- 253 EIGENVALUES OF SPECIAL MATRICES * 253 EIGENVECTORS ----- 260 SOME DEFINITIONS AND EXAMPLES ----- 260 EIGENVALUES OF POWERS OF A MATRIX ----- 267 EIGENVALUES AND EIGENVECTORS OF REAL SYMMETRIC MATRICES * 269 SOME PROPERTIES OF COMPLEX NUMBERS AND MATRICES IN THE COMPLEX FIELDS ----- 280 COMPLEX NUMBERS * 280 GEOMETRY OF COMPLEX NUMBERS ----- 281 ALGEBRA OF COMPLEX NUMBERS ----- 283 N-TH ROOTS OF UNITY ----- 286 VECTORS WITH COMPLEX ELEMENTS * 289 MATRICES WITH COMPLEX ELEMENTS ----- 291 MORE PROPERTIES OF MATRICES IN THE COMPLEX FIELD ----- 298 EIGENVALUES OF SYMMETRIC AND HERMITIAN MATRICES * 298 DEFINITENESS OF MATRICES ----- 307 COMMUTATIVE MATRICES * 310 SOME APPLICATIONS OF MATRICES AND DETERMINANTS * 325 INTRODUCTION ----- 325 DIFFERENCE AND DIFFERENTIAL EQUATIONS ----- 325 FIBONACCI SEQUENCE AND DIFFERENCE EQUATIONS ----- 325 POPULATION GROWTH ----- 331 DIFFERENTIAL EQUATIONS AND THEIR SOLUTIONS ----- 332 JACOBIANS OF MATRIX TRANSFORMATIONS AND FUNCTIONS OF MATRIX ARGUMENT ----- 341 JACOBIANS OF MATRIX TRANSFORMATIONS * 342 FUNCTIONS OF MATRIX ARGUMENT ----- 348 SOME TOPICS FROM STATISTICS ----- 354 PRINCIPAL COMPONENTS ANALYSIS ----- 354 REGRESSION ANALYSIS AND MODEL BUILDING ----- 358 DESIGN TYPE MODELS ----- 362 CANONICAL CORRELATION ANALYSIS ----- 364 PROBABILITY MEASURES AND MARKOV PROCESSES * 371 INVARIANCE OF PROBABILITY MEASURES ----- 372 DISCRETE TIME MARKOV PROCESSES AND TRANSITION PROBABILITIES ----- 374 MAXIMA/MINIMA PROBLEMS ----- 381 TAYLOR SERIES ----- 382 OPTIMIZATION OF QUADRATIC FORMS ----- 387 5.5.3 OPTIMIZATION OF A QUADRATIC FORM WITH QUADRATIC FORM CONSTRAINTS * 389 5.5.4 OPTIMIZATION OFA QUADRATIC FORM WITH LINEAR CONSTRAINTS * 390 5.5.5 OPTIMIZATION OF BILINEAR FORMS WITH QUADRATIC CONSTRAINTS * 392 5.6 LINEAR PROGRAMMING AND NONLINEAR LEAST SQUARES * 398 5.6.1 THE SIMPLEX METHOD * 400 5.6.2 NONLINEAR LEAST SQUARES * 406 5.6.3 MARQUARDTS METHOD 408 5.6.4 MATHAI-KATIYAR PROCEDURE * 410 5.7 A LIST OF SOME MORE PROBLEMS FROM PHYSICAL, ENGINEERING AND SOCIAL SCIENCES * 411 5.7.1 TURBULENT FLOW OFA VISCOUS FLUID * 411 5.7.2 COMPRESSIBLE FLOW OF VISCOUS FLUIDS * 412 5.7.3 HEAT LOSS IN A STEEL ROD * 412 5.7.4 SMALL OSCILLATIONS ----- 413 5.7.5 INPUT-OUTPUT ANALYSIS * 414 6 MATRIX SERIES AND ADDITIONAL PROPERTIES OF MATRICES * - 417 6.0 INTRODUCTION * 417 6.1 MATRIX POLYNOMIALS * 417 6.1.1 LAGRANGE INTERPOLATING POLYNOMIAL * 418 6.1.2 A SPECTRAL DECOMPOSITION OF A MATRIX * 420 6.1.3 AN APPLICATION IN STATISTICS * 422 6.2 MATRIX SEQUENCES AND MATRIX SERIES * 424 6.2.1 MATRIX SEQUENCES * 424 6.2.2 MATRIX SERIES ----- 426 6.2.3 MATRIX HYPERGEOMETRIC SERIES * 429 6.2.4 THE NORM OF A MATRIX * 430 6.2.5 COMPATIBLE NORMS * 434 6.2.6 MATRIX POWER SERIES AND RATE OF CONVERGENCE * 435 6.2.7 AN APPLICATION IN STATISTICS * 435 6.3 SINGULAR VALUE DECOMPOSITION OFA MATRIX * 438 6.3.1 A SINGULAR VALUE DECOMPOSITION * 440 6.3.2 CANONICAL FORM OFA BILINEAR FORM * 443 REFERENCES * 447 INDEX * 449
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spellingShingle	Mathai, Arakaparampil M. 1935- Haubold, Hans J. 1951- Linear algebra a course for physicists and engineers Lineare Algebra (DE-588)4035811-2 gnd
subject_GND	(DE-588)4035811-2
title	Linear algebra a course for physicists and engineers
title_auth	Linear algebra a course for physicists and engineers
title_exact_search	Linear algebra a course for physicists and engineers
title_full	Linear algebra a course for physicists and engineers Arak M. Mathai and Hans J. Haubold
title_fullStr	Linear algebra a course for physicists and engineers Arak M. Mathai and Hans J. Haubold
title_full_unstemmed	Linear algebra a course for physicists and engineers Arak M. Mathai and Hans J. Haubold
title_short	Linear algebra
title_sort	linear algebra a course for physicists and engineers
title_sub	a course for physicists and engineers
topic	Lineare Algebra (DE-588)4035811-2 gnd
topic_facet	Lineare Algebra
url	https://www.doabooks.org/doab?func=fulltext&uiLanguage=en&rid=25453 https://doi.org/10.1515/9783110562507 https://www.degruyter.com/view/product/495839 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029847849&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT mathaiarakaparampilm linearalgebraacourseforphysicistsandengineers AT hauboldhansj linearalgebraacourseforphysicistsandengineers AT walterdegruytergmbhcokg linearalgebraacourseforphysicistsandengineers

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