Matrix differential calculus with applications in statistics and econometrics:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
1999
|
| Ausgabe: | Rev. ed., reprinted |
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagwörter: | |
| Links: | http://www.loc.gov/catdir/description/wiley037/98053556.html http://www.loc.gov/catdir/toc/onix04/98053556.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008607575&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVIII, 395 S. graph. Darst. |
| ISBN: | 0471986321 047198633X |
Internformat
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Datensatz im Suchindex
| _version_ | 1819330583441965056 |
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| adam_text | MATRIX DIFFERENTIAL CALCULUS WITH APPLICATIONS IN STATISTICS AND
ECONOMETRICS REVISED EDITION JAN. R. MAGNUS CENTERJOR ECONOMIC RESEARCH,
TILBURG UNIVERSITY AND HEINZ NEUDECKER CESARO, SCHAGEN JOHN WILEY & SONS
CHICHESTER * NEW YORK * WEINHEIM * BRISBANE * SINGAPORE * TORONTO
CONTENTS PREFACE PREFACE TO THE FAST REVISED PRINTING PREFACE TO THE
SECOND REVISED PRINTING PART ONE * MATRICES 1 BASIC PROPERTIES OF
VECTORS AND MATRICES 1 INTRODUCTION, 3 2 SETS, 3 3 MATRICES: ADDITION
AND MULTIPLICATION, 4 4 THE TRANSPOSE OF A MATRIX, 5 5 SQUARE MATRICES,
6 6 LINEAR FORMS AND QUADRATIC FORMS, 7 7 THE RANK OFA MATRIX, 8 8 THE
INVERSE, 9 9 THE DETERMINANT, 9 10 THE TRACE, 10 11 PARTITIONED
MATRICES, 11 12 COMPLEX MATRICES, 13 13 CIGENVALUES AND EIGENVECTORS, 13
14 SCHUR S DECOMPOSITION THEOREM, 16 15 THE JORDAN DECOMPOSITION, 17 16
THE SINGULAR-VALUE DECOMPOSITION, 18 17 FURT HER RESULTS CONCERNING
EIGENVALUES, 19 18 POSITIVE (SEMI)DEFINITE MATRICES, 21 19 THREEFURTHER
RESULTSFOR POSITIVE DEFINITE MATRICES, 23 20 A USEFUL RESULT, 24
MISCELLANEOUS EXERCISES, 25 BIBILIOGRAPHICAL NOTES, 26 2 KRONECKER
PRODUCTS, THE VEC OPERATOR AND THE MOORE-PENROSE INVERSE 1 INTRODUCTION,
27 2 THE KRONECKER PRODUCT, 27 3 EIGENVALUES OF A KRONECKER PRODUCT, 28
4 THE VEC OPERATOR, 30 5 THE MOORE-PENROSE (MP) INVERSE, 3 2 6 EXISTENCE
AND UNIQUENESS OF THE MP INVERSE, 32 7 SOME PROPERTIES OFTHE MP INVERSE,
33 8 FURTHER PROPERTIES, 34 9 THE SOLUTION OF LINEAR EQUATION SYSTEMS,
36 MISCELLANEOUS EXERCISES, 38 BIBLIOGRAPHICAL NOTES, 39 3 MISCELLANEOUS
MATRIX RESULTS 1 INTRODUCTION, 40 2 77IE ADJOINT MATRIX, 40 3 PROOF OF
THEOREM 7, 41 4 7 VO RESULTS CONCERNING BORDERED DETERMINANTS, 43 5 77IE
MATRIX EQUATION AX = 0, 44 6 77IE HADAMARD PRODUCT, 45 7 77»E
COMMUTATION MATRIX K MN , 46 8 77IE DUPLICATION MATRIX D N , 48 9
RELATIONSHIP BETWEEN D* +I AND D*, I, 50 10 RELATIONSHIP BETWEEN D* +L
AND D*, II, 52 11 CONDITIONS FOR A QUADRATIC FORM TO BE POSITIVE
(NEGATIVE) SUBJECT LINEAR CONSTRAINTS, 53 12 NECESSARY AND SUFFICIENT
CONDITIONS FOR R(A:B) = R{A) + R(B), 56 13 THE BORDERED GRAMIAN MATRIX,
57 14 THE EQUATIONS X 1 A + X 2 B = G I ,X L B = G 2 , 60 MISCELLANEOUS
EXERCISES, 62 BIBLIOGRAPHICAL NOTES, 62 PART TWO * DIFFERENTIALS: THE
THEORY 4 MATHEMATICAL PRELIMINARIES 1 INTRODUCTION, 65 2 INTERIOR POINTS
AND ACCUMULATION POINTS, 65 3 OPEN AND CIOSED SETS, 66 4 77IE
BOLZANO-WEIERSTRASS THEOREM, 69 5 FUNCTIONS, 70 6 77IE /IMIT OF
AFUNCTION, 70 7 CONTINUOUS FUNCTIONS AND COMPACTNESS, 71 8 CONUEX SETS,
72 9 CONUEX AND CONCAVE FUNCTIONS, 75 BIBLIOGRAPHICAL NOTES, 77 CONTENTS
VU 5 DIFFERENTIALS AND DIFFERENTIABILITY 78 1 INTRODUCTION, 78 2
CONTINUITY, 78 3 DIFFERENTIABILITY AND LINEAR APPROXIMATION, 80 4 THE
DIFFERENTIAL OF A VECTOR FUNCTION, 82 5 UNIQUENESS OF THE DIFFERENTIAL,
84 6 CONTINUITY OF DIFFERENTIABLE FUNCTIONS, 84 7 PARTIAL DERIVATIVES,
85 8 THEFIRST IDENTIFICATION THEOREM, 87 9 EXISTENCE OF THE
DIFFERENTIAL, I, 88 10 EXISTENCE OF THE DIFFERENTIAL, II, 89 11
CONTINUOUS DIFFERENTIABILITY, 91 12 THE CHAIN RULE, 91 13 CAUCHY
INVARIANCE, 93 14 THE MEAN-VALUE THEOREM FOR REAL-VALUED FUNCTIONS, 93
15 MATRIX FUNCTIONS, 94 16 SOME REMARKS ON NOTATION, 96 MISCELLANEOUS
EXERCISES, 98 BIBLIOGRAPHICAL NOTES, 98 6 THE SECOND DIFFERENTIAL 99 1
INTRODUCTION, 99 2 SECOND-ORDER PARTIAL DERIVATIVES, 99 3 77IE HESSIAN
MATRIX, 100 4 TWICE DIFFERENTIABILITY AND SECOND-ORDER APPROXIMATION, 1,
101 5 DEFINITION OF TWICE DIFFERENTIABILITY, 102 6 THE SECOND
DIFFERENTIAL, 103 7 (COLUMN) SYMMETRY OF THE HESSIAN MATRIX, 105 8 THE
SECOND IDENTIFICATION THEOREM, 107 9 TWICE DIFFERENTIABILITY AND
SECOND-ORDER APPROXIMATION, II, 108 10 CHAIN RULE FOR HESSIAN MATRICES,
110 11 THE ANALOGUE FOR SECOND DIFFERENTIALS, 111 12 TAYLOR S THEOREM
FOR REAL-VALUED FUNCTIONS, 112 13 HIGHER-ORDER DIFFERENTIALS, 113 14
MATRIX FUNCTIONS, 114 BIBLIOGRAPHICAL NOTES, 115 7 STATIC OPTIMIZATION
116 1 INTRODUCTION, 116 2 UNCONSTRAINED OPTIMIZATION, 116 3 THE
EXISTENCE OF ABSOLUTE EXTREMA, 118 4 NECESSARY CONDITIONS FOR A LOCAL
MINIMUM, 11 9 5 SUFFICIENT CONDITIONS FOR A LOCAL MINIMUM:
FIRST-DERIVATIVE TEST, 121 6 SUFFICIENT CONDITIONS FOR A LOCAL MINIMUM:
SECOND-DERIVATIVE TEST, 122 7 CHARACTERIZATION OF DIFFERENTIABLE CONVEX
FUNCTIONS, 124 8 CHARACTERIZATION OF TWICE DIFFERENTIABLE CONVEX
FUNCTIONS, 127 9 SUFFICIENT CONDITIONS FOR AN ABSOLUTE MINIMUM, 128 10
MONOTONIE TRANSFORMATIONS, 129 11 OPTIMIZATION SUBJEET TO CONSTRAINTS,
130 12 NECESSARY CONDITIONS FOR A LOCAL MINIMUM UNDER CONSTRAINTS, 131
13 SUFFICIENT CONDITIONS FOR A LOCAL MINIMUM UNDER CONSTRAINTS, 135 14
SUFFICIENT CONDITIONS FOR AN ABSOLUTE MINIMUM UNDER CONSTRAINTS, 139 15
V4 NOTE ON CONSTRAINTS IN MATRIX FORM, 140 16 ECONOMIC INTERPRETATION OF
LAGRANGE MULTIPLIERS, 141 APPENDIX: THE IMPLICIT FUNETION THEOREM, 142
BIBLIOGRAPHICAL NOTES, 144 PART THREE * DIFFERENTIALS: THE PRACTICE 8
SOME IMPORTANT DIFFERENTIALS 1 INTRODUCTION, 147 2 FUNDAMENTAL RULES OF
DIFFERENTIAL CALCULUS, 147 3 THE DIFFERENTIAL OF A DETERMINANT, 149 4
THE DIFFERENTIAL OF AN INVERSE, 151 5 THE DIFFERENTIAL OF THE
MOORE-PENROSE INVERSE, 152 6 THE DIFFERENTIAL OF THE ADJOINT MATRIX, 155
7 ON DIFFERENTIATING EIGENVALUES AND EIGENVECTORS, 157 8 THE
DIFFERENTIAL OF EIGENVALUES AND EIGENVECTORS: THE REAL SYMMETRIE CASE,
158 9 THE DIFFERENTIAL OF EIGENVALUES AND EIGENVECTORS: THE GENERAL
COMPLEX CASE, 161 10 TWO ALTERNATIVE EXPRESSIONS FOR 11 THE SECOND
DIFFERENTIAL OF THE EIGENVALUE FUNETION, 166 12 MULTIPLE EIGENVALUES,
167 MISCELLANEOUS EXERCISES, 167 BIBLIOGRAPHICAL NOTES, 169 9
FIRST-ORDER DIFFERENTIALS AND JACOBIAN MATRICES 1 INTRODUCTION, 170 2
CLASSIFICATION, 170 3 BAD NOTATION, 171 4 GOOD NOTATION, 173 5
IDENTIFICATION OF JACOBIAN MATRICES, 174 6 THE FIRST IDENTIFICATION
TABLE, 175 7 PARTITIONING OF THE DERIVATIVE, 175 8 SCALAR FUNCTIONS OF A
VECTOR, 176 9 SCALAR FUNCTIONS OF A MATRIX, I: TRACE, 177 10 SCALAR
FUNCTIONS OF A MATRIX, II: DETERMINANT, 178 11 SCALAR FUNCTIONS OF A
MATRIX, 111: EIGENVALUE, 180 12 TWO EXAMPLES OF VECTOR FUNCTIONS, 181 13
MATRIX FUNCTIONS, 182 14 KRONECKER PRODUCTS, 184 15 SOME OTHER PROBLEMS,
185 BIBLIOGRAPHICAL NOTES, 187 10 SECOND-ORDER DIFFERENTIALS AND HESSIAN
MATRICES 1 INTRODUCTION, 188 2 THE HESSIAN MATRIX OF A MATRIX FUNCTION,
188 3 IDENTIFICATION OF HESSIAN MATRICES, 189 4 77IE SECOND
IDENTIFICATION TABLE, 190 5 AN EXPLICIT FORMULA FOR THE HESSIAN MATRIX,
19 1 6 SCALAR FUNCTIONS, 192 7 VECTOR FUNCTIONS, 194 8 MATRIX FUNCTIONS,
I, 194 9 MATRIX FUNCTIONS, II, 195 PART FOUR * INEQUALITIES 11
INEQUALITIES 1 INTRODUCTION, 199 2 77IE CAUDRY-SC/IWARZ INEQUALITY, 199
3 MATRIX ANALOGUES OF THE CAUCHY-SCHWARZ INEQUALITY, 201 4 77IE THEOREM
OF THE ARITHMETIC AND GEOMETRIC MEANS, 202 5 77IE RAYLEIGH QUOTIENT, 203
6 CONCAVITY OF X T , CONVEXITY OF X*, 204 7 VARIATIONAL DESCRIPTION OF
EIGENVALUES, 205 8 FISCHEFS MIN-MAX THEOREM, 206 9 MONOTONICITY OF THE
EIGENVALUES, 208 10 77IE POINCARE SEPARATION THEOREM, 209 11 TWO
COROLLARIES OF POINCARE S THEOREM, 210 12 FURTHER CONSEQUENCES OF THE
POINCARE THEOREM, 211 13 MULTIPLICATIVE VERSION, 21 2 14 77JE MAXIMUM OF
A BILINEAR FORM, 213 15 HADAMARD S INEQUALITY, 214 16 /IN INTERLUDE:
KARAMATA S INEQUALITY, 215 17 KARAMATA S INEQUALITY APPLIED TO
EIGENVALUES, 217 18 AN INEQUALITY CONCERNING POSITIVE SEMIDEFINITE
MATRICES 19 A REPRESENTATION THEOREMFOR (ZA P ) LLP , 218 20 A
REPRESENTATION THEOREM FOR (TR A ) ILP , 219 21 HOLDER S INEQUALITY, 220
22 CONCAVITY OF LOG A , 222 23 MINKOWSKIS INEQUALITY, 223 24
QUASILINEAR REPRESENTATION OF A { , 224 25 MINKOWSKI S DETERMINANT
THEOREM, 227 26 WEIGHTED MEANS OF ORDER P, 227 27 SCHLOEMILCH S
INEQUALITY, 229 28 CURVATURE PROPERTIES OF M*{X, A), 230 29 LEAST
SQUARES, 232 30 GENERALIZED LEAST SQUARES, 233 31 RESTRICTED LEAST
SQUARES, 233 32 RESTRICTED LEAST SQUARES: MATRIX VERSION, 235
MISCELLANEOUS EXERCISES, 236 BIBLIOGRAPHICAL NOTES, 240 PART FIVE * THE
LINEAR MODEL 12 STATISTICAL PRELIMINARIES 1 INTRODUCTION, 243 2 77IE
CUMULATIVE DISTRIBUTION FUNCTION, 243 3 77IE YOIM DENSITY FUNCTION, 244
4 EXPECTATIONS, 244 5 VARIANCE AND COVARIANCE, 245 6 INDEPENDENCE OFTWO
RANDOM VARIABLES (VECTORS), 247 7 INDEPENDENCE OF N RANDOM VARIABLES
(VECTORS), 249 8 SAMPLING, 249 9 77IE ONE-DIMENSIONAL NORMAL
DISTRIBUTION, 249 10 THE MULTIVARIATE NORMAL DISTRIBUTION, 250 11
ESTIMATION, 252 MISCELLANEOUS EXERCISES, 253 BIBLIOGRAPHICAL NOTES, 25 3
13 THE LINEAR REGRESSION MODEL 1 INTRODUCTION, 254 2 AFFINE
MINIMUM-TRACE UNBIASED ESTIMATION, 255 3 77IE GAUSS-MARKOV THEOREM, 256
4 77IE METHOD OF LEAST SQUARES, 258 5 AITKEN S THEOREM, 259 6
MULTICOLLINEARITY, 261 7 ESTIMABLE FUNCTIONS, 263 CONTENTS XI 8 LINEAR
CONSTRAINTS: THE CASE M{R ) ^J1 {X 264 9 LINEAR CONSTRAINTS: THE
GENERAL CASE, 267 10 LINEAR CONSTRAINTS: THE CASE JT(R )C^J((X ) = {0},
270 11 A SINGULAR VARIANCE MATRIX: THE CASE J((X) ^M(V), 271 12 A
SINGULAR VARIANCE MATRIX: THE CASE R(X V + X) = R(X), 273 13 A SINGULAR
VARIANCE MATRIX: THE GENERAL CASE, I, 214 14 EXPLICIT AND IMPLICIT
LINEAR CONSTRAINTS, 275 15 THE GENERAL LINEAR MODEL, I, 277 16 A
SINGULAR VARIANCE MATRIX: THE GENERAL CASE, II, 27 8 17 THE GENERAL
LINEAR MODEL, II, 281 18 GENERALIZED LEAST SQUARES, 282 19 RESTRICTED
LEAST SQUARES, 283 MISCEILANEOUS EXERCISES, 285 BIBLIOGRAPHICAL NOTES,
286 14 FURTHER TOPICS IN THE LINEAR MODEL 287 1 INTRODUCTION, 287 2 BEST
QUADRATIC UNBIASED ESTIMATION OF A 2 , 287 3 77IE BEST QUADRATIC AND
POSITIVE UNBIASED ESTIMATOR OF A 2 , 288 4 THE BEST QUADRATIC UNBIASED
ESTIMATOR OFA 2 , 290- 5 BEST QUADRATIC INVARIANT ESTIMATION OFA 2 , 292
6 THE BEST QUADRATIC AND POSITIVE INVARIANT ESTIMATOR OF A 2 , 293 7 THE
BEST QUADRATIC INVARIANT ESTIMATOR OFA 2 , 294 8 BEST QUADRATIC UNBIASED
ESTIMATION IN THE MULTIVARIATE NORMAL CASE, 295 9 BOUNDSFOR THE BIAS OF
THE LEAST SQUARES ESTIMATOR OFA 2 ,1, 297 10 BOUNDSFOR THE BIAS OF THE
LEAST SQUARES ESTIMATOR OFA 2 , II, 299 11 THE PREDICTION OF
DISTURBANCES, 300 12 PREDICTORS THAT ARE BEST LINEAR UNBIASED WITH
SCALAR VARIANCE MATRIX (BLUS), 301 13 PREDICTORS THAT ARE BEST LINEAR
UNBIASED WITH FIXED VARIANCE MATRIX (BLUF), L, 303 14 PREDICTORS THAT
ARE BEST LINEAR UNBIASED WITH FIXED VARIANCE MATRIX (BLUF), II, 305 15
LOCAL SENSITIVITY OF THE POSTERIOR MEAN, 306 16 LOCAL SENSITIVITY OF THE
POSTERIOR PRECISION, 308 BIBLIOGRAPHICAL NOTES, 309 PART SIX *
APPLICATIONS TO MAXIMUM LIKELIHOOD ESTIMATION 15 MAXIMUM LIKELIHOOD
ESTIMATION 313 1 INTRODUCTION, 313 2 THE METHOD OF MAXIMUM LIKELIHOOD
(ML), 313 3 ML ESTIMATION OF THE MULTIVARIATE NORMAL DISTRIBUTION, 314
XLL 4 IMPLICIT VERSUS EXPLICIT TREATMENT OF SYMMETRY, 316 5 THE
TREATMENT OF POSITIVE DEFINITENESS, 317 6 THE INFORMATION MATRIX, 317 7
ML ESTIMATION OF THE MULTIVARIATE NORMAL DISTRIBUTION WITH DISTINCT
MEANS, 319 8 THE MULTIVARIATE LINEAR REGRESSION MODEL, 320 9 THE
ERRORS-IN-VARIABLES MODEL, 322 10 THE NONLINEAR REGRESSION MODEL WITH
NORMAL ERRORS, 324 11 A SPECIAL CASE: FUNCTIONAL INDEPENDENCE OF MEAN
PARAMETERS AND VARIANCE PARAMETERS, 326 12 GENERALIZATION OF THEOREM 6,
327 MISCELLANEOUS EXERCISES, 329 BIBLIOGRAPHICAL NOTES, 330 16
SIMULTANEOUS EQUATIONS 1 INTRODUCTION, 331 2 THE SIMULTANEOUS EQUATIONS
MODEL, 331 3 THE IDENTIFICATION PROBLEM, 333 4 IDENTIFICATION WITH
LINEAR CONSTRAINTS ON B AND V ONLY, 334 5 IDENTIFICATION WITH LINEAR
CONSTRAINTS ON B, Y AND L, 335 6 NONLINEAR CONSTRAINTS, 337 7
FULL-INFORMATION MAXIMUM LIKELIHOOD (FIML): THE INFORMATION MATRIX
(GENERAL CASE), 337 8 FULL-INFORMATION MAXIMUM LIKELIHOOD (FIML): THE
ASYMPTOTIC VARIANCE MATRIX (SPECIAL CASE), 33 9 9 LIMITED-INFORMATION
MAXIMUM LIKELIHOOD (LIML): THE FIRST-ORDER CONDITIONS, 342 10
LIMITED-INFORMATION MAXIMUM LIKELIHOOD (LIML): THE INFORMATION MATRIX,
344 11 LIMITED-INFORMATION MAXIMUM LIKELIHOOD (LIML): THE ASYMPTOTIC
VARIANCE MATRIX, 346 BIBLIOGRAPHICAL NOTES, 351 17 TOPICS IN
PSYCHOMETRICS 1 INTRODUCTION, 352 2 POPULATION PRINCIPAL COMPONENTS, 353
3 OPTIMALITY OF PRINCIPAL COMPONENTS, 353 4 A RELATED RESULT, 355 5
SAMPLE PRINCIPAL COMPONENTS, 356 6 OPTIMALITY OF SAMPLE PRINCIPAL
COMPONENTS, 358 7 SAMPLE ANALOGUE OF THEOREM 3, 358 8 ONE-MODE COMPONENT
ANALYSIS, 358 CONTENTS 9 RELATIONSHIP BETWEEN ONE-MODE COMPONENT
ANALYSIS AND SAMPLE PRINCIPAL COMPONENTS, 361 10 TWO-MODE COMPONENT
ANALYSIS, 362 11 MULTIMODE COMPONENT ANALYSIS, 363 12 FACTOR ANALYSIS,
366 13 A ZIGZAG ROUTINE, 369 14 A NEWTON-RAPHSON ROUTINE, 370 15
KAISER S VARIMAX METHOD, 373 16 CANONICAL CORRELATIONS AND VARIATES IN
THE POPULATION, 376 BIBLIOGRAPHICAL NOTES, 378 BIBLIOGRAPHY INDEX OF
SYMBOLS SUBJECT INDEX
|
| any_adam_object | 1 |
| author | Magnus, Jan R. 1948- Neudecker, Heinz 1933- |
| author_GND | (DE-588)170162664 (DE-588)133363392 |
| author_facet | Magnus, Jan R. 1948- Neudecker, Heinz 1933- |
| author_role | aut aut |
| author_sort | Magnus, Jan R. 1948- |
| author_variant | j r m jr jrm h n hn |
| building | Verbundindex |
| bvnumber | BV012666615 |
| callnumber-first | Q - Science |
| callnumber-label | QA188 |
| callnumber-raw | QA188.M345 1999 |
| callnumber-search | QA188.M345 1999 |
| callnumber-sort | QA 3188 M345 41999 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 300 SK 220 SK 400 |
| ctrlnum | (OCoLC)245681793 (DE-599)BVBBV012666615 |
| dewey-full | 512.9/43421 512.9434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/434 21 512.9434 |
| dewey-search | 512.9/434 21 512.9434 |
| dewey-sort | 3512.9 3434 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | Rev. ed., reprinted |
| format | Book |
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| id | DE-604.BV012666615 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:34:15Z |
| institution | BVB |
| isbn | 0471986321 047198633X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008607575 |
| oclc_num | 245681793 |
| open_access_boolean | |
| owner | DE-703 DE-521 DE-83 DE-11 |
| owner_facet | DE-703 DE-521 DE-83 DE-11 |
| physical | XVIII, 395 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spellingShingle | Magnus, Jan R. 1948- Neudecker, Heinz 1933- Matrix differential calculus with applications in statistics and econometrics Statistik Matrices Differential calculus Statistics Econometrics Differentialrechnung (DE-588)4012252-9 gnd Matrixfunktion (DE-588)4169117-9 gnd Matrix Mathematik (DE-588)4037968-1 gnd Differential (DE-588)4149768-5 gnd Matrizenrechnung (DE-588)4126963-9 gnd Ökonometrie (DE-588)4132280-0 gnd |
| subject_GND | (DE-588)4012252-9 (DE-588)4169117-9 (DE-588)4037968-1 (DE-588)4149768-5 (DE-588)4126963-9 (DE-588)4132280-0 |
| title | Matrix differential calculus with applications in statistics and econometrics |
| title_auth | Matrix differential calculus with applications in statistics and econometrics |
| title_exact_search | Matrix differential calculus with applications in statistics and econometrics |
| title_full | Matrix differential calculus with applications in statistics and econometrics Jan R. Magnus and Heinz Neudecker |
| title_fullStr | Matrix differential calculus with applications in statistics and econometrics Jan R. Magnus and Heinz Neudecker |
| title_full_unstemmed | Matrix differential calculus with applications in statistics and econometrics Jan R. Magnus and Heinz Neudecker |
| title_short | Matrix differential calculus with applications in statistics and econometrics |
| title_sort | matrix differential calculus with applications in statistics and econometrics |
| topic | Statistik Matrices Differential calculus Statistics Econometrics Differentialrechnung (DE-588)4012252-9 gnd Matrixfunktion (DE-588)4169117-9 gnd Matrix Mathematik (DE-588)4037968-1 gnd Differential (DE-588)4149768-5 gnd Matrizenrechnung (DE-588)4126963-9 gnd Ökonometrie (DE-588)4132280-0 gnd |
| topic_facet | Statistik Matrices Differential calculus Statistics Econometrics Differentialrechnung Matrixfunktion Matrix Mathematik Differential Matrizenrechnung Ökonometrie |
| url | http://www.loc.gov/catdir/description/wiley037/98053556.html http://www.loc.gov/catdir/toc/onix04/98053556.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008607575&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT magnusjanr matrixdifferentialcalculuswithapplicationsinstatisticsandeconometrics AT neudeckerheinz matrixdifferentialcalculuswithapplicationsinstatisticsandeconometrics |