Generalized vectorization, cross-products, and matrix calculus:
This book presents the reader with new operators and matrices that arise in the area of matrix calculus. The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2013
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| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBG01 Volltext |
| Zusammenfassung: | This book presents the reader with new operators and matrices that arise in the area of matrix calculus. The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned into submatrices. Studying the properties of these submatrices facilitates achieving new results for the original matrices themselves. Different concepts of matrix derivatives are presented and transformation principles linking these concepts are obtained. One of these concepts is used to derive new matrix calculus results, some involving the new operators and others the derivatives of the operators themselves. The last chapter contains applications of matrix calculus, including optimization, differentiation of log-likelihood functions, iterative interpretations of maximum likelihood estimators and a Lagrangian multiplier test for endogeneity |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 24 Feb 2016) |
| Beschreibung: | 1 online resource (xi, 267 pages) |
| ISBN: | 9781139424400 |
| DOI: | 10.1017/CBO9781139424400 |
Internformat
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| 246 | 1 | 3 | |a Generalized Vectorization, Cross-Products, & Matrix Calculus |
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| 505 | 8 | |a 1. Mathematical prerequisites -- 2. Zero-one matrices -- 3. Elimination and duplication matrices -- 4. Matrix calculus -- 5. New matrix calculus results -- 6. Applications | |
| 520 | |a This book presents the reader with new operators and matrices that arise in the area of matrix calculus. The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned into submatrices. Studying the properties of these submatrices facilitates achieving new results for the original matrices themselves. Different concepts of matrix derivatives are presented and transformation principles linking these concepts are obtained. One of these concepts is used to derive new matrix calculus results, some involving the new operators and others the derivatives of the operators themselves. The last chapter contains applications of matrix calculus, including optimization, differentiation of log-likelihood functions, iterative interpretations of maximum likelihood estimators and a Lagrangian multiplier test for endogeneity | ||
| 650 | 4 | |a Matrices | |
| 650 | 4 | |a Vector analysis | |
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Datensatz im Suchindex
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| author | Turkington, Darrell A. 1947- |
| author_GND | (DE-588)1012336387 |
| author_facet | Turkington, Darrell A. 1947- |
| author_role | aut |
| author_sort | Turkington, Darrell A. 1947- |
| author_variant | d a t da dat |
| building | Verbundindex |
| bvnumber | BV043695792 |
| classification_rvk | SK 220 |
| collection | ZDB-20-CBO |
| contents | 1. Mathematical prerequisites -- 2. Zero-one matrices -- 3. Elimination and duplication matrices -- 4. Matrix calculus -- 5. New matrix calculus results -- 6. Applications |
| ctrlnum | (ZDB-20-CBO)CR9781139424400 (OCoLC)847033272 (DE-599)BVBBV043695792 |
| dewey-full | 515/.63 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.63 |
| dewey-search | 515/.63 |
| dewey-sort | 3515 263 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139424400 |
| format | Electronic eBook |
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| id | DE-604.BV043695792 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:32:45Z |
| institution | BVB |
| isbn | 9781139424400 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029108362 |
| oclc_num | 847033272 |
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| owner_facet | DE-473 DE-BY-UBG DE-12 DE-92 |
| physical | 1 online resource (xi, 267 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBG_PDA_CBO |
| publishDate | 2013 |
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| publisher | Cambridge University Press |
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| spelling | Turkington, Darrell A. 1947- Verfasser (DE-588)1012336387 aut Generalized vectorization, cross-products, and matrix calculus Darrell A. Turkington Generalized Vectorization, Cross-Products, & Matrix Calculus Cambridge Cambridge University Press 2013 1 online resource (xi, 267 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 24 Feb 2016) 1. Mathematical prerequisites -- 2. Zero-one matrices -- 3. Elimination and duplication matrices -- 4. Matrix calculus -- 5. New matrix calculus results -- 6. Applications This book presents the reader with new operators and matrices that arise in the area of matrix calculus. The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned into submatrices. Studying the properties of these submatrices facilitates achieving new results for the original matrices themselves. Different concepts of matrix derivatives are presented and transformation principles linking these concepts are obtained. One of these concepts is used to derive new matrix calculus results, some involving the new operators and others the derivatives of the operators themselves. The last chapter contains applications of matrix calculus, including optimization, differentiation of log-likelihood functions, iterative interpretations of maximum likelihood estimators and a Lagrangian multiplier test for endogeneity Matrices Vector analysis Vektoranalysis (DE-588)4191992-0 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 s Vektoranalysis (DE-588)4191992-0 s 1\p DE-604 Erscheint auch als Druckausgabe 978-1-107-03200-2 Erscheint auch als Druckausgabe 978-1-107-44872-8 https://doi.org/10.1017/CBO9781139424400 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Turkington, Darrell A. 1947- Generalized vectorization, cross-products, and matrix calculus 1. Mathematical prerequisites -- 2. Zero-one matrices -- 3. Elimination and duplication matrices -- 4. Matrix calculus -- 5. New matrix calculus results -- 6. Applications Matrices Vector analysis Vektoranalysis (DE-588)4191992-0 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| subject_GND | (DE-588)4191992-0 (DE-588)4037968-1 |
| title | Generalized vectorization, cross-products, and matrix calculus |
| title_alt | Generalized Vectorization, Cross-Products, & Matrix Calculus |
| title_auth | Generalized vectorization, cross-products, and matrix calculus |
| title_exact_search | Generalized vectorization, cross-products, and matrix calculus |
| title_full | Generalized vectorization, cross-products, and matrix calculus Darrell A. Turkington |
| title_fullStr | Generalized vectorization, cross-products, and matrix calculus Darrell A. Turkington |
| title_full_unstemmed | Generalized vectorization, cross-products, and matrix calculus Darrell A. Turkington |
| title_short | Generalized vectorization, cross-products, and matrix calculus |
| title_sort | generalized vectorization cross products and matrix calculus |
| topic | Matrices Vector analysis Vektoranalysis (DE-588)4191992-0 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| topic_facet | Matrices Vector analysis Vektoranalysis Matrix Mathematik |
| url | https://doi.org/10.1017/CBO9781139424400 |
| work_keys_str_mv | AT turkingtondarrella generalizedvectorizationcrossproductsandmatrixcalculus AT turkingtondarrella generalizedvectorizationcrossproductsmatrixcalculus |