Matrix algebra for applied economics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Wiley
2001
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| Series: | Wiley series in probability and statistics
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| Subjects: | |
| Online Access: | Publisher description Table of contents Inhaltsverzeichnis |
| Physical Description: | XX, 402 S. |
| ISBN: | 0471322075 |
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| adam_text | MATRIX ALGEBRA FOR APPLIED ECONOMICS SHAYLE R. SEARLE DEPARTMENTS OF
BIOMETRICS AND OF STATISTICAL SCIENCE CORNELL UNIVERSITY
LOISSCHERTZWILLETT FOOD AND RESOURCE ECONOMICS DEPARTMENT UNIVERSITY OF
FLORIDA A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC.
CONTENTS LIST OF CHARTERS V PREFACE XIX I BASICS 1 1 INTRODUCTION 3 1.1
THE SCOPE OF MATRIX ALGEBRA 3 1.2 USING COMPUTERS FOR MATRIX ARITHMETIC
4 1.3 A MATRIX IS AN ARRAY 5 1.4 SUBSCRIPT NOTATION 6 1.5 SUMMATION
NOTATION 7 1.6 DOT NOTATION 11 1.7 DEFINITION OF A MATRIX 11 1.8 SOME
BASIC SPECIAL FORMS 12 A. SQUARE MATRICES 12 B. DIAGONAL MATRICES 13 C.
IDENTITY MATRICES 13 D. TRIANGULAER MATRICES 13 E. NULL MATRICES 13 F.
EQUAL MATRICES 14 G. VECTORS 14 H. SEALARS 14 1.9 DESCRIPTION BY
ELEMENTS 15 1.10 NOTATION 15 1.11 EXAMPLES AND ILLUSTRATIONS 16 1.12
EXERCISES 16 VU VLLL CONTENTS 2 BASIC MATRIX OPERATIONS 21 2.1
TRANSPOSING A MATRIX 21 A. A REFLEXIVE OPERATION 22 B. VECTORS 22 C.
SYMMETRIE MATRICES 22 D. NOTATION: IFF AND NSC 24 2.2 PARTITIONED
MATRICES 24 A. AN EXAMPLE 24 B. GENERAL SPEEIFICATION 26 C. TRANSPOSING
A PARTITIONED MATRIX 26 D. PARTITIONING INTO VECTORS 27 2.3 TRACE OF A
SQUARE MATRIX 27 2.4 MATRIX ADDITION 28 A. TRANSPOSING A SUM 29 B. TRACE
OF A SUM 30 C. SCALAR MULTIPLICATION 30 2.5 MATRIX SUBTRACTION 30 2.6
MULTIPLICATION 33 A. INNER PRODUET OF TWO VECTORS 33 B. A MATRIX-VECTOR
PRODUET 34 C. A MATRIX-MATRIX PRODUET 36 D. EXISTENCE OF MATRIX PRODUETS
39 E. PRODUCTS WITH VECTORS 40 F. PRODUCTS WITH SCALARS 43 G. PRODUCTS
WITH NULL MATRICES 43 H. PRODUCTS WITH DIAGONAL MATRICES 43 I. PRODUCTS
WITH IDENTITY MATRICES 44 J. TRANSPOSE OF A PRODUET 44 K. TRACE OF A
PRODUET 45 1. POWERS OF A MATRIX 46 M. MULTIPLYING PARTITIONED MATRICES
48 N. HADAMARD PRODUETS 49 2.7 THE LAWS OF ALGEBRA 50 A. ASSOCIATIVE
LAWS 50 B. DISTRIBUTIVE LAW 51 C. COMMUTATIVE LAWS 51 2.8 CONTRASTS WITH
SCALAR ALGEBRA 52 2.9 EXERCISES 53 3 SPECIAL MATRICES 63 3.1 LINEAR
TRANSFORMATIONS 63 CONTENTS IX 3.2 SYMMETRY: SOME BASIC OUTCOMES 64 A.
VERIFYING SYMMETRY 64 B. PRODUCT OF SYMMETRIE MATRICES 64 C. PROPERTIES
OF AA AND A A 65 D. PRODUCTS OF VECTORS 66 E. SUMS OF OUTER PRODUETS 67
F. ELEMENTARY VECTORS 67 G. SKEW-SYMMETRIC MATRICES 68 3.3 SUMMING
VECTORS AND THEIR PRODUCTS 68 3.4 IDEMPOTENT MATRICES 71 3.5 ORTHOGONAL
MATRICES 72 3.6 QUADRATIC FORMS 73 A. DEFINITION 73 B. THE MATRIX A IS
ALWAYS SYMMETRIE IN X AX ... 74 C. NUMERICAL EXAMPLE 75 D. EXPLICIT
EXPANSION 76 E. BILINEAR FORM 76 F. POSITIVE (AND NEGATIVE) DEFINITE
MATRICES 76 - I. POSITIVE DEFINITENESS 77 - II. NEGATIVE DEFINITENESS 78
3.7 VARIANCE-COVARIANCE MATRICES 78 3.8 CORRELATION MATRICES 79 3.9 LDU
DECOMPOSITION 80 3.10 EXERCISES 81 4 DETERMINANTS 87 4.1 INTRODUCTION 87
4.2 EXPANSION BY MINORS 90 4.3 ELEMENTARY EXPANSIONS 93 A. DETERMINANT
OF A TRANSPOSE 93 B. TWO ROWS THE SAME 94 C. ADDING TO A ROW A MULTIPLE
OF ANOTHER ROW . . . . 94 D. ADDING A ROW TO A MULTIPLE OF A ROW 97 E.
PRODUCTS 97 - I. DETERMINANT OF A TRIANGULAER MATRIX . . 98 - II.
REDUCING A DETERMINANT TO TRIANGULAER FORM 98 - III. TWO PARTITIONED
DETERMINANTS 99 - IV. VERIFICATION OF THE PRODUCT RULE 99 - V.
EXTENSIONS TO RECTANGULAR MATRICES . . . 100 X CONTENTS - VI. USEFUL
COROLLARIES 101 F. CRAMER S RULE FOR LINEAR EQUATIONS 101 - I.
ILLUSTRATION: INPUT-OUTPUT EQUATIONS . . 102 - II. ILLUSTRATION: SUPPLY
AND DEMAND . . . . 102 4.4 ELEMENTARY ROW OPERATIONS 103 A. DEFINITIONS
103 B. EACTORIZATION 105 C. ONE ROW BEING A MULTIPLE OF ANOTHER 105 D.
ROW (COLUMN) OF ZEROS 106 E. INTERCHANGING ROWS (COLUMNS) 106 4.5
DIAGONAL EXPANSION 106 A. NOTATION FOR MINORS 106 B. DETERMINANT OF A +
D 107 C. PRINCIPAL MINORS 107 D. SPECIAL CASE: A + AI 108 4.6 LAPLACE
EXPANSION 108 4.7 SUMS AND DIFFERENCES OF DETERMINANTS 110 4.8 EXERCISES
111 5 INVERSE MATRICES 117 5.1 INTRODUCTION 117 5.2 EXISTENCE AND
UNIQUENESS OF AN INVERSE 118 A. EXISTENCE 118 B. UNIQUENESS 119 5.3
RECTANGULAR MATRICES 119 5.4 COFACTORS 120 5.5 DERIVING THE INVERSE 121
A. FOR A MATRIX OF ORDER 3 121 B. GENERAL CASE 123 C. ADJUGATE MATRIX
123 5.6 PROPERTIES OF THE INVERSE 124 5.7 SOME SIMPLE SPECIAL CASES 124
A. INVERSES OF ORDER 2 125 B. DIAGONAL MATRICES 125 C. ORTHOGONAL
MATRICES 125 5.8 SOLVING LINEAR EQUATIONS 126 5.9 ALGEBRAIC
SIMPLIFICATIONS 127 5.10 PARTITIONED MATRICES 129 5.11 LEFT AND RIGHT
INVERSES 130 5.12 USING COMPUTING SOFTWARE 131 CONTENTS XI A. PROBLEMS
OF ACCURACY 131 B. ALGORITHMIC ERROR 131 C. ROUNDING ERROR 132 - I.
ADDITION 132 - II. INVERTING A MATRIX 132 - III. SOLVING LINEAR
EQUATIONS 134 - IV. ROUNDING AT DATA INPUT 136 D. SPEED 136 5.13
EXERCISES 137 II NECESSARY THEORY 145 6 LINEARLY (IN)DEPENDENT VECTORS
147 6.1 LINEAR COMBINATIONS OF VECTORS 147 6.2 LINEAR DEPENDENCE AND
INDEPENDENCE 149 A. DEFINITIONS 149 - I. LINEARLY DEPENDENT VECTORS 149
- II. LINEARLY INDEPENDENT VECTORS 150 B. GENERAL PROPERTIES 151 - I.
SETS OF VECTORS 151 - II. SOME COEFFICIENTS ZERO 151 - III. EXISTENCE
AND NON-UNIQUENESS OF NON- ZERO COEFFICIENTS 152 - IV. NULL VECTORS 152
6.3 LINEARLY DEPENDENT VECTORS 152 A. AT LEAST TWO COEFFICIENTS ARE
NON-ZERO 152 B. VECTORS ARE LINEAR COMBINATIONS OF OTHERS . . . . 153 C.
ZERO DETERMINANTS 153 D. INVERSE MATRICES 154 E. TESTING FOR DEPENDENCE
(SIMPLE CASES) 154 6.4 LINEARLY INDEPENDENT (LIN) VECTORS 156 A. NONZERO
DETERMINANTS AND INVERSE MATRICES . . . 156 B. LINEAR COMBINATIONS OF
LIN VECTORS 156 C. MAXIMUM NUMBER OF LIN VECTORS 157 6.5 EXERCISES 159 7
RANK 161 7.1 NUMBER OF LIN ROWS AND COLUMNS 161 7.2 RANK OF A MATRIX 163
XII CONTENTS 7.3 RANK AND INVERSE MATRICES 164 7.4 ELEMENTARY OPERATORS
165 A. ROW OPERATIONS 166 B. TRANSPOSES 166 C. COLUMN OPERATIONS 166 D.
INVERSES 167 7.5 RANK AND THE ELEMENTARY OPERATORS 168 A. RANK 168 B.
PRODUCTS OF ELEMENTARY OPERATORS 168 C. EQUIVALENCE 168 7.6 CALCULATING
THE RANK OF A MATRIX 169 A. SOME SPECIAL LIN VECTORS 169 B. CALCULATING
RANK 170 7.7 PERMUTATION MATRICES 171 7.8 MATRIX FACTORIZATION 172 A.
MATRICES WITH LINEARLY DEPENDENT COLUMNS . . . . 172 B. FULL-RANK
FACTORIZATION 173 C. USING PERMUTATION MATRICES 174 7.9 RESULTS ON RANK
175 7.10 VECTOR SPACES 175 A. EUCLIDEAN SPACE 175 B. VECTOR SPACES 176
C. SPANNING SETS AND BASES 177 D. MANY SPACES OF ORDER N 177 E.
SUB-SPACES 178 F. RANGE AND NULL SPACE OF A MATRIX 178 7.11 EXERCISES
179 8 CANONICAL FORMS 185 8.1 INTRODUCTION 185 8.2 EQUIVALENT CANONICAL
FORM 185 A. EQUIVALENT MATRICES 185 B. REDUCTION TO EQUIVALENT CANONICAL
FORM 186 - I. EXAMPLE 186 - II. THE GENERAL CASE 188 C. NON-UNIQUENESS
OF P AND Q 189 D. EXISTENCE AND NON-SINGULARITY OF P AND Q . . . . 189
E. FUELL RANK FACTORIZATION 190 8.3 CONGRUENT REDUCTION 191 A. SYMMETRIE
MATRICES 191 CONTENTS XIII B. EXAMPLE 193 8.4 QUADRATIC FORMS 194 8.5
FUELL RANK FACTORING A SYMMETRIE MATRIX . . . . . . . . 195 8.6
NON-NEGATIVE DEFINITE MATRICES 196 A. DIAGONAL ELEMENTS AND PRINCIPAL
MINORS 196 B. CONGRUENT CANONICAL FORM 197 C. FULL-RANK FACTORIZATION
197 D. USEFUL PRODUCTA 197 8.7 PROOFS OF RESULTS ON RANK 198 8.8
EXERCISES 200 9 GENERALIZED INVERSES 203 9.1 MOORE-PENROSE INVERSE 203
9.2 GENERALIZED INVERSES 204 9.3 DERIVING A GENERALIZED INVERSE 205 A.
USING THE DIAGONAL FORM 205 B. INVERTING A SUB-MATRIX 206 C. A MORE
GENERAL INVERSION 207 9.4 ARBITRARINESS IN A GENERALIZED INVERSE 207 9.5
SYMMETRIE MATRICES 208 A. TWO GENERAL RESULTS 208 B. NON-NEGATIVE
DEFINITE MATRICES 209 C. THE MATRIX X X 209 D. MOORE-PENROSE INVERSES
210 9.6 EXERCISES 210 10 SOLVING LINEAR EQUATIONS 213 10.1 EQUATIONS
HAVING MANY SOLUTIONS 213 10.2 CONSISTENT EQUATIONS 215 A. DEFINITION
215 B. EXISTENCE OF SOLUTIONS 215 C. TESTING FOR CONSISTENCY 216 10.3
EQUATIONS WITH ONLY ONE SOLUTION 217 10.4 SOLUTIONS USING A GENERALIZED
INVERSE 218 A. OBTAINING ONE SOLUTION 218 B. OBTAINING MANY SOLUTIONS
219 10.5 COMPLETE EXAMPLE 221 10.6 EXERCISES 223 XIV CONTENTS 11
EIGENROOTSANDEIGENVECTORS 227 11.1 BASIC EQUATION 227 A. NON-NULL
VECTORS 227 B. DERIVING ROOTS 228 C. DEFINITIONS 228 D. CAYLEY-HAMILTON
THEOREM 229 11.2 ELEMENTARY PROPERTIES OF EIGENROOTS 230 A. EIGENROOTS
OF POWERS OF A MATRIX 230 B. EIGENROOTS OF A SCALAR MULTIPLE OF A MATRIX
. . . . 230 C. EIGENROOTS OF POLYNOMIALS 231 D. SUM AND PRODUCT OF
EIGENROOTS 231 E. EIGENROOTS OF PARTICULAR MATRICES 231 - I. TRANSPOSED
231 - II. ORTHOGONAL 231 - III. IDEMPOTENT 231 11.3 CALCULATING
EIGENVECTORS 232 11.4 SIMILAR CANONICAL FORM 233 11.5 ASYMMETRIE
MATRICES, MULTIPLE ROOTS 235 A. MULTIPLE ROOTS 235 B. VECTORS FOR
MULTIPLE ROOTS 236 C. DIAGONABILITY THEOREM 236 11.6 SYMMETRIE MATRICES
237 A. EIGENROOTS ALL REAL 237 B. SYMMETRIE MATRICES ARE DIAGONABLE 238
C. EIGENVECTORS ARE ORTHOGONAL 238 D. CANONICAL FORM UNDER ORTHOGONAL
SIMILARITY . . . 238 E. RANK EQUALS NUMBER OF NON-ZERO EIGENROOTS . . .
239 F. SPECTRAL DECOMPOSITION 240 G. NON-NEGATIVE DEFINITE (N.N.D.)
MATRICES 240 11.7 DOMINANT EIGENROOTS 241 11.8 SINGULAR-VALUE
DECOMPOSITION 242 11.9 EXERCISES 243 12 MISCELLANEA 249 12.1 ORTHOGONAL
MATRICES: A SUMMARY 249 12.2 IDEMPOTENT MATRICES: A SUMMARY 250 12.3
MATRIX AL + 6J: A SUMMARY 250 12.4 NON-NEGATIVE DEFINITE MATRICES 251
12.5 CANONICAL FORMS AND OTHER DECOMPOSITIONS 252 A. EQUIVALENT
CANONICAL FORM 252 B. CONGRUENT CANONICAL FORM 252 CONTENTS XV C.
SIMILAR CANONICAL FORM 252 D. ORTHOGONAL SIMILAR CANONICAL FORM 253 E.
SINGULAR-VALUE DECOMPOSITION 253 F. SPECTRAL DECOMPOSITION 253 G. THE
LDU AND LU DECOMPOSITIONS . 253 12.6 MATRIX FUNCTIONS 254 A. FUNCTIONS
OF MATRICES 254 B. MATRICES OF FUNCTIONS 254 12.7 DIRECT SUMS AND
PRODUCTS 254 A. DIRECT SUMS 255 B. DIRECT PRODUCTS 255 12.8 VEC AND VECH
OPERATORS 256 12.9 DIFFERENTIAL CALCULUS 258 A. SEALARS 258 B. VECTORS
259 C. QUADRATIC FORMS 260 D. INVERSES 260 E. TRACES 261 F. DETERMINANTS
261 G. JACOBIANS 263 H. HESSIANS 265 12.10 EXERCISES 266 III WORKING
WITH MATRICES 269 13 APPLYING LINEAR EQUATIONS 271 13.1 COST
MINIMIZATION IN A FIRM 271 13.2 CONSUMER S UTILITY AND EXPENDITURE 274
13.3 INPUT-OUTPUT ANALYSIS 276 13.4 EXERCISES 279 14 REGRESSION ANALYSIS
285 14.1 SIMPLE REGRESSION MODEL 285 A. MODEL SPEEIFICATION 285 B. DATA
286 C. ESTIMATION 287 14.2 MULTIPLE LINEAR REGRESSION 289 A. THEMODEL
289 B. THE MEANING OF LINEAR 290 XVI CONTENTS 14.3 ESTIMATION 290 A. THE
GENERAL RESULT 290 B. USING DEVIATIONS FROM MEANS 292 14.4 STATISTICAL
MODEL 296 14.5 UNBIASEDNESS AND VARIANCES 296 14.6 ESTIMATING THE
VARIANCE 297 14.7 PARTITIONING THE TOTAL SUM OF SQUARES 299 14.8
MULTIPLE CORRELATION 302 14.9 TESTING LINEAR HYPOTHESES 303 A. STATING A
HYPOTHESIS 303 B. THE F-STATISTIC 304 C. EQUIVALENT STATEMENTS OF A
HYPOTHESIS 305 D. HYPOTHESES NOT INVOLVING THE INTERCEPT 306 E. SPECIAL
CASES 307 14.10 PREDICTING AND FORECASTING 308 A. THE TRADITIONAL
PREDICTOR 308 B. FORECASTING 309 14.11 ANALYSIS OF VARIANCE 309 14.12
CONFIDENCE INTERVALS 312 14.13 THE NO-INTERCEPT MODEL 312 14.14
SIMULTANEOUS EQUATIONS 314 A. MODEL 314 B. IDENTIFICATION 316 C. METHODS
OF ESTIMATION 317 14.15 APPENDIX 318 14.16 EXERCISES 319 15 LINEAR
STATISTICAL MODELS 323 15.1 GENERAL DESCRIPTION 323 A. ILLUSTRATION
(LINEAR MODEL) 323 B. MODEL 324 15.2 NORMAL EQUATIONS 326 A. GENERAL
FORM 326 B. MANY SOLUTIONS 328 15.3 SOLVING THE NORMAL EQUATIONS 328 A.
GENERALIZED INVERSES OF X X 328 B. SOLUTIONS 329 15.4 EXPECTED VALUES
AND VARIANCES 330 15.5 PREDICTED Y- VALUES 331 15.6 ESTIMATING THE
RESIDUAL VARIANCE 331 CONTENTS XVII A. ERROR SUM OF SQUARES 331 B.
SOLUTIONS OBTAINED WITHOUT USING A G 333 C. EXPECTED VALUE 333 D.
ESTIMATION 334 15.7 PAXTITIONING THE TOTAL SUM OF SQUARES 334 15.8
COEFFICIENT OF DETERMINATION 335 15.9 ANALYSIS OF VARIANCE 336 15.10
ESTIMABLE FUNCTIONS 339 15.11 TESTING LINEAR HYPOTHESES 341 15.12
CONFIDENCE INTERVALS 345 15.13 THE ILLUSTRATION GENERALIZED 345 15.14
APPENDIX: RESULTS ON QUADRATIC FORMS 348 A. EXPECTED VALUE 348 B.
CHI-SQUARE DISTRIBUTIONS . 348 C. INDEPENDENCE 348 D. INDEPENDENCE WITH
LINEAR FORMS 348 E. J-DISTRIBUTIONS 348 15.15 EXERCISES 349 16 LINEAR
PROGRAMMING 351 16.1 THE MAXIMIZATION PROBLEM 351 A. ILLUSTRATION
(PROFIT MAXIMIZATION) 351 B. MATRIX FORMULATION 353 C. GRAPHICAL
SOLUTION 354 D. EXTREME POINTS 356 E. SLACK VARIABLES 357 F. BASIC
SOLUTION 358 16.2 THE MINIMIZATION PROBLEM 360 A. MATRIX FORMULATION 360
B. ILLUSTRATION 360 C. SURPLUS VARIABLES 361 16.3 SIMPLEX METHOD 362
16.4 RELATED TOPICS 363 A. CHANGING A MINIMIZATION PROBLEM TO A
MAXIMIZATION PROBLEM 363 B. MIXED CONSTRAINTS 363 C. CHANGING THE
DIRECTION OF AN INEQUALITY 363 D. UNCONSTRAINED VARIABLES 364 E. THE
DUAL PROBLEM 364 16.5 APPLICATIONS OF LINEAR PROGRAMMING 367 XVM
CONTENTS 16.6 EXERCISES 370 17 MARKOV CHAIN MODELS 373 17.1 ILLUSTRATION
(MARKET SHARE) 373 17.2 STEADY-STATE PROBABILITIES 375 17.3 TIRANSIENT
STATES 378 17.4 PERIODIC OR CYCLING BEHAVIOR 378 17.5 RECURRENT SETS 379
17.6 EXISTENCE OF STEADY-STATE PROBABILITIES 380 17.7 REWARDS IN MARKOV
CHAINS 381 17.8 ADDITIONAL APPLICATIONS OF MARKOV CHAINS 384 17.9
EXERCISES 385 REFERENCES 389 INDEX 393
|
| any_adam_object | 1 |
| author | Searle, S. R. 1928-2013 Willett, Lois Schertz |
| author_GND | (DE-588)128417137 |
| author_facet | Searle, S. R. 1928-2013 Willett, Lois Schertz |
| author_role | aut aut |
| author_sort | Searle, S. R. 1928-2013 |
| author_variant | s r s sr srs l s w ls lsw |
| building | Verbundindex |
| bvnumber | BV013898866 |
| callnumber-first | H - Social Science |
| callnumber-label | HB135 |
| callnumber-raw | HB135.S38 2001 |
| callnumber-search | HB135.S38 2001 |
| callnumber-sort | HB 3135 S38 42001 |
| callnumber-subject | HB - Economic Theory and Demography |
| classification_rvk | QH 140 SK 220 SK 980 |
| classification_tum | MAT 150f |
| ctrlnum | (OCoLC)248434101 (DE-599)BVBBV013898866 |
| dewey-full | 330/.01/5129434 330/.01/512943421 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 330 - Economics |
| dewey-raw | 330/.01/5129434 330/.01/5129434 21 |
| dewey-search | 330/.01/5129434 330/.01/5129434 21 |
| dewey-sort | 3330 11 75129434 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV013898866 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:54:05Z |
| institution | BVB |
| isbn | 0471322075 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009511361 |
| oclc_num | 248434101 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-N2 DE-29T DE-521 DE-11 DE-384 |
| owner_facet | DE-703 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-N2 DE-29T DE-521 DE-11 DE-384 |
| physical | XX, 402 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Searle, S. R. 1928-2013 Verfasser (DE-588)128417137 aut Matrix algebra for applied economics Shayle R. Searle ; Lois Schertz Willett New York Wiley 2001 XX, 402 S. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Theorie Wirtschaft Ökonometrisches Modell Economics, Mathematical Economics -- Econometric models Matrices Anwendung (DE-588)4196864-5 gnd rswk-swf Wirtschaftswissenschaften (DE-588)4066528-8 gnd rswk-swf Matrizenalgebra (DE-588)4139347-8 gnd rswk-swf Matrizenalgebra (DE-588)4139347-8 s Anwendung (DE-588)4196864-5 s Wirtschaftswissenschaften (DE-588)4066528-8 s DE-604 Willett, Lois Schertz Verfasser aut http://www.loc.gov/catdir/description/wiley035/2001026759.html Publisher description http://www.loc.gov/catdir/toc/wiley021/2001026759.html Table of contents GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009511361&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Searle, S. R. 1928-2013 Willett, Lois Schertz Matrix algebra for applied economics Theorie Wirtschaft Ökonometrisches Modell Economics, Mathematical Economics -- Econometric models Matrices Anwendung (DE-588)4196864-5 gnd Wirtschaftswissenschaften (DE-588)4066528-8 gnd Matrizenalgebra (DE-588)4139347-8 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4066528-8 (DE-588)4139347-8 |
| title | Matrix algebra for applied economics |
| title_auth | Matrix algebra for applied economics |
| title_exact_search | Matrix algebra for applied economics |
| title_full | Matrix algebra for applied economics Shayle R. Searle ; Lois Schertz Willett |
| title_fullStr | Matrix algebra for applied economics Shayle R. Searle ; Lois Schertz Willett |
| title_full_unstemmed | Matrix algebra for applied economics Shayle R. Searle ; Lois Schertz Willett |
| title_short | Matrix algebra for applied economics |
| title_sort | matrix algebra for applied economics |
| topic | Theorie Wirtschaft Ökonometrisches Modell Economics, Mathematical Economics -- Econometric models Matrices Anwendung (DE-588)4196864-5 gnd Wirtschaftswissenschaften (DE-588)4066528-8 gnd Matrizenalgebra (DE-588)4139347-8 gnd |
| topic_facet | Theorie Wirtschaft Ökonometrisches Modell Economics, Mathematical Economics -- Econometric models Matrices Anwendung Wirtschaftswissenschaften Matrizenalgebra |
| url | http://www.loc.gov/catdir/description/wiley035/2001026759.html http://www.loc.gov/catdir/toc/wiley021/2001026759.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009511361&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT searlesr matrixalgebraforappliedeconomics AT willettloisschertz matrixalgebraforappliedeconomics |