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Cover: 9780387783567 | Matrix Algebra From a Statistician's Perspective | David A. Harville
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Matrix Algebra From a Statistician's Perspective
Taschenbuch von David A. Harville
Sprache: Englisch

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Beschreibung
Matrix algebra plays a very important role in statistics and in many other dis- plines. In many areas of statistics, it has become routine to use matrix algebra in thepresentationandthederivationorveri?cationofresults. Onesuchareaislinear statistical models; another is multivariate analysis. In these areas, a knowledge of matrix algebra isneeded in applying important concepts, as well as instudying the underlying theory, and is even needed to use various software packages (if they are to be used with con?dence and competence). On many occasions, I have taught graduate-level courses in linear statistical models. Typically, the prerequisites for such courses include an introductory (- dergraduate) course in matrix (or linear) algebra. Also typically, the preparation provided by this prerequisite course is not fully adequate. There are several r- sons for this. The level of abstraction or generality in the matrix (or linear) algebra course may have been so high that it did not lead to a ¿working knowledge¿ of the subject, or, at the other extreme, the course may have emphasized computations at the expense of fundamental concepts. Further, the content of introductory courses on matrix (or linear) algebra varies widely from institution to institution and from instructor to instructor. Topics such as quadratic forms, partitioned matrices, and generalized inverses that play an important role in the study of linear statistical models may be covered inadequately if at all.
Matrix algebra plays a very important role in statistics and in many other dis- plines. In many areas of statistics, it has become routine to use matrix algebra in thepresentationandthederivationorveri?cationofresults. Onesuchareaislinear statistical models; another is multivariate analysis. In these areas, a knowledge of matrix algebra isneeded in applying important concepts, as well as instudying the underlying theory, and is even needed to use various software packages (if they are to be used with con?dence and competence). On many occasions, I have taught graduate-level courses in linear statistical models. Typically, the prerequisites for such courses include an introductory (- dergraduate) course in matrix (or linear) algebra. Also typically, the preparation provided by this prerequisite course is not fully adequate. There are several r- sons for this. The level of abstraction or generality in the matrix (or linear) algebra course may have been so high that it did not lead to a ¿working knowledge¿ of the subject, or, at the other extreme, the course may have emphasized computations at the expense of fundamental concepts. Further, the content of introductory courses on matrix (or linear) algebra varies widely from institution to institution and from instructor to instructor. Topics such as quadratic forms, partitioned matrices, and generalized inverses that play an important role in the study of linear statistical models may be covered inadequately if at all.
Über den Autor
David A. Harville is a research staff member in the Mathematical Sciences Department of the IBM T.J.Watson Research Center. Prior to joining the Research Center he spent ten years as a mathematical statistician in the Applied Mathematics Research Laboratory of the Aerospace Research Laboratories (at Wright-Patterson, FB, Ohio, followed by twenty years as a full professor in the Department of Statistics at Iowa State University. He has extensive experience in the area of linear statistical models, having taught (on numberous occasions) M.S.and Ph.D.level courses on that topic,having been the thesis adviser of 10 Ph.D. students,and having authored over 60 research articles. His work has been recognized by his election as a Fellow of the American Statistical Association and the Institute of Mathematical Statistics and as a member of the International Statistical Institute and by his having served as an associate editor of Biometrics and of the Journal of the American Statistical Association.
Zusammenfassung

This book offers thorough and unified coverage of the fundamental concepts of matrix algebra. Its approach will make it particularly suited to those with an interest in statistics or related disciplines. But it does much more, too: it is enlightening in specialized areas of statistics such as linear statistical models and multivariate analysis. David Harville, a former associate editor of the Journal of the American Statistical Association, ensures that the style and level of presentation make the contents accessible to a broad audience. It includes a number of very useful results that have, up to now, only been available from relatively obscure sources, and for which detailed proofs are provided. It also contains numerous exercises, the solutions to which can be found in the author's Matrix Algebra: Exercises and Solutions.

Inhaltsverzeichnis
Matrices.- Submatrices and Partitioned Matrices.- Linear Dependence and Independence.- Linear Spaces: Row and Column Spaces.- Trace of a (Square) Matrix.- Geometrical Considerations.- Linear Systems: Consistency and Compatibility.- Inverse Matrices.- Generalized Inverses.- Idempotent Matrices.- Linear Systems: Solutions.- Projections and Projection Matrices.- Determinants.- Linear, Bilinear, and Quadratic Forms.- Matrix Differentiation.- Kronecker Products and the Vec and Vech Operators.- Intersections and Sums of Subspaces.- Sums (and Differences) of Matrices.- Minimization of a Second-Degree Polynomial (in n Variables) Subject to Linear Constraints.- The Moore-Penrose Inverse.- Eigenvalues and Eigenvectors.- Linear Transformations.- Erratum.
Details
Erscheinungsjahr: 2008
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 656
Inhalt: xvi
634 S.
ISBN-13: 9780387783567
ISBN-10: 0387783563
Sprache: Englisch
Herstellernummer: 12231102
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Harville, David A.
Auflage: 1st ed. 1997. 2nd printing 2008
Hersteller: Springer New York
Springer US, New York, N.Y.
Maße: 235 x 155 x 36 mm
Von/Mit: David A. Harville
Erscheinungsdatum: 27.06.2008
Gewicht: 0,978 kg
preigu-id: 101830643
Über den Autor
David A. Harville is a research staff member in the Mathematical Sciences Department of the IBM T.J.Watson Research Center. Prior to joining the Research Center he spent ten years as a mathematical statistician in the Applied Mathematics Research Laboratory of the Aerospace Research Laboratories (at Wright-Patterson, FB, Ohio, followed by twenty years as a full professor in the Department of Statistics at Iowa State University. He has extensive experience in the area of linear statistical models, having taught (on numberous occasions) M.S.and Ph.D.level courses on that topic,having been the thesis adviser of 10 Ph.D. students,and having authored over 60 research articles. His work has been recognized by his election as a Fellow of the American Statistical Association and the Institute of Mathematical Statistics and as a member of the International Statistical Institute and by his having served as an associate editor of Biometrics and of the Journal of the American Statistical Association.
Zusammenfassung

This book offers thorough and unified coverage of the fundamental concepts of matrix algebra. Its approach will make it particularly suited to those with an interest in statistics or related disciplines. But it does much more, too: it is enlightening in specialized areas of statistics such as linear statistical models and multivariate analysis. David Harville, a former associate editor of the Journal of the American Statistical Association, ensures that the style and level of presentation make the contents accessible to a broad audience. It includes a number of very useful results that have, up to now, only been available from relatively obscure sources, and for which detailed proofs are provided. It also contains numerous exercises, the solutions to which can be found in the author's Matrix Algebra: Exercises and Solutions.

Inhaltsverzeichnis
Matrices.- Submatrices and Partitioned Matrices.- Linear Dependence and Independence.- Linear Spaces: Row and Column Spaces.- Trace of a (Square) Matrix.- Geometrical Considerations.- Linear Systems: Consistency and Compatibility.- Inverse Matrices.- Generalized Inverses.- Idempotent Matrices.- Linear Systems: Solutions.- Projections and Projection Matrices.- Determinants.- Linear, Bilinear, and Quadratic Forms.- Matrix Differentiation.- Kronecker Products and the Vec and Vech Operators.- Intersections and Sums of Subspaces.- Sums (and Differences) of Matrices.- Minimization of a Second-Degree Polynomial (in n Variables) Subject to Linear Constraints.- The Moore-Penrose Inverse.- Eigenvalues and Eigenvectors.- Linear Transformations.- Erratum.
Details
Erscheinungsjahr: 2008
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 656
Inhalt: xvi
634 S.
ISBN-13: 9780387783567
ISBN-10: 0387783563
Sprache: Englisch
Herstellernummer: 12231102
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Harville, David A.
Auflage: 1st ed. 1997. 2nd printing 2008
Hersteller: Springer New York
Springer US, New York, N.Y.
Maße: 235 x 155 x 36 mm
Von/Mit: David A. Harville
Erscheinungsdatum: 27.06.2008
Gewicht: 0,978 kg
preigu-id: 101830643
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