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Título : Linear Algebra and Linear Models Tipo de documento: documento electrónico Autores: Ravindra B. Bapat ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2012 Otro editor: Imprint: Springer Colección: Universitext, ISSN 0172-5939 Número de páginas: VIII, 167 p. 1 illus Il.: online resource ISBN/ISSN/DL: 978-1-4471-2739-0 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Statistics Linear and Multilinear Algebras, Theory Statistical Methods for Business/Economics/Mathematical Finance/Insurance Clasificación: 51 Matemáticas Resumen: Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing. The emphasis is on the approach using generalized inverses. Topics such as the multivariate normal distribution and distribution of quadratic forms are included. For this third edition, the material has been reorganised to develop the linear algebra in the first six chapters, to serve as a first course on linear algebra that is especially suitable for students of statistics or for those looking for a matrix theoretic approach to the subject. Other key features include: • coverage of topics such as rank additivity, inequalities for eigenvalues and singular values; • a new chapter on linear mixed models; • over seventy additional problems on rank: the matrix rank is an important and rich topic with connections to many aspects of linear algebra such as generalized inverses, idempotent matrices and partitioned matrices. This text is aimed primarily at advanced undergraduate and first-year graduate students taking courses in linear algebra, linear models, multivariate analysis and design of experiments. A wealth of exercises, complete with hints and solutions, help to consolidate understanding. Researchers in mathematics and statistics will also find the book a useful source of results and problems Nota de contenido: Vector Spaces and Subspaces -- Rank, Inner Product and Nonsingularity -- Eigenvalues and Positive Definite Matrices -- Generalized Inverses -- Inequalities for Eigenvalues and Singular Values -- Rank Additivity and Matrix Partial Orders -- Linear Estimation -- Tests of Linear Hypotheses -- Linear Mixed Models -- Miscellaneous Topics -- Additional Exercises on Rank En línea: http://dx.doi.org/10.1007/978-1-4471-2739-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32721 Linear Algebra and Linear Models [documento electrónico] / Ravindra B. Bapat ; SpringerLink (Online service) . - London : Springer London : Imprint: Springer, 2012 . - VIII, 167 p. 1 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4471-2739-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Statistics Linear and Multilinear Algebras, Theory Statistical Methods for Business/Economics/Mathematical Finance/Insurance Clasificación: 51 Matemáticas Resumen: Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing. The emphasis is on the approach using generalized inverses. Topics such as the multivariate normal distribution and distribution of quadratic forms are included. For this third edition, the material has been reorganised to develop the linear algebra in the first six chapters, to serve as a first course on linear algebra that is especially suitable for students of statistics or for those looking for a matrix theoretic approach to the subject. Other key features include: • coverage of topics such as rank additivity, inequalities for eigenvalues and singular values; • a new chapter on linear mixed models; • over seventy additional problems on rank: the matrix rank is an important and rich topic with connections to many aspects of linear algebra such as generalized inverses, idempotent matrices and partitioned matrices. This text is aimed primarily at advanced undergraduate and first-year graduate students taking courses in linear algebra, linear models, multivariate analysis and design of experiments. A wealth of exercises, complete with hints and solutions, help to consolidate understanding. Researchers in mathematics and statistics will also find the book a useful source of results and problems Nota de contenido: Vector Spaces and Subspaces -- Rank, Inner Product and Nonsingularity -- Eigenvalues and Positive Definite Matrices -- Generalized Inverses -- Inequalities for Eigenvalues and Singular Values -- Rank Additivity and Matrix Partial Orders -- Linear Estimation -- Tests of Linear Hypotheses -- Linear Mixed Models -- Miscellaneous Topics -- Additional Exercises on Rank En línea: http://dx.doi.org/10.1007/978-1-4471-2739-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32721 Ejemplares
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Título : Linear Optimization Problems with Inexact Data Tipo de documento: documento electrónico Autores: M. Fiedler ; SpringerLink (Online service) ; J. Nedoma ; Jaroslav Ramík ; J. Rohn ; Karel Zimmermann Editorial: Boston, MA : Springer US Fecha de publicación: 2006 Número de páginas: XVI, 214 p. 5 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-32698-6 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Game Mathematical optimization Operations research Management science Optimization Linear and Multilinear Algebras, Theory Theory, Economics, Social Behav. Sciences Research, Science Clasificación: 51 Matemáticas Resumen: Linear programming attracted the interest of mathematicians during and after World War II when the first computers were constructed and methods for solving large linear programming problems were sought in connection with specific practical problems—for example, providing logistical support for the U.S. Armed Forces or modeling national economies. Early attempts to apply linear programming methods to solve practical problems failed to satisfy expectations. There were various reasons for the failure. One of them, which is the central topic of this book, was the inexactness of the data used to create the models. This phenomenon, inherent in most pratical problems, has been dealt with in several ways. At first, linear programming models used "average” values of inherently vague coefficients, but the optimal solutions of these models were not always optimal for the original problem itself. Later researchers developed the stochastic linear programming approach, but this too has its limitations. Recently, interest has been given to linear programming problems with data given as intervals, convex sets and/or fuzzy sets. The individual results of these studies have been promising, but the literature has not presented a unified theory. Linear Optimization Problems with Inexact Data attempts to present a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework. Audience This book is intended for postgraduate or graduate students in the areas of operations research, optimization theory, linear algebra, interval analysis, reliable computing, and fuzzy sets. The book will also be useful for researchers in these respective areas Nota de contenido: Matrices -- Solvability of systems of interval linear equations and inequalities -- Interval linear programming -- Linear programming with set coefficients -- Fuzzy linear optimization -- Interval linear systems and optimization problems over max-algebras En línea: http://dx.doi.org/10.1007/0-387-32698-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34797 Linear Optimization Problems with Inexact Data [documento electrónico] / M. Fiedler ; SpringerLink (Online service) ; J. Nedoma ; Jaroslav Ramík ; J. Rohn ; Karel Zimmermann . - Boston, MA : Springer US, 2006 . - XVI, 214 p. 5 illus : online resource.
ISBN : 978-0-387-32698-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Game Mathematical optimization Operations research Management science Optimization Linear and Multilinear Algebras, Theory Theory, Economics, Social Behav. Sciences Research, Science Clasificación: 51 Matemáticas Resumen: Linear programming attracted the interest of mathematicians during and after World War II when the first computers were constructed and methods for solving large linear programming problems were sought in connection with specific practical problems—for example, providing logistical support for the U.S. Armed Forces or modeling national economies. Early attempts to apply linear programming methods to solve practical problems failed to satisfy expectations. There were various reasons for the failure. One of them, which is the central topic of this book, was the inexactness of the data used to create the models. This phenomenon, inherent in most pratical problems, has been dealt with in several ways. At first, linear programming models used "average” values of inherently vague coefficients, but the optimal solutions of these models were not always optimal for the original problem itself. Later researchers developed the stochastic linear programming approach, but this too has its limitations. Recently, interest has been given to linear programming problems with data given as intervals, convex sets and/or fuzzy sets. The individual results of these studies have been promising, but the literature has not presented a unified theory. Linear Optimization Problems with Inexact Data attempts to present a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework. Audience This book is intended for postgraduate or graduate students in the areas of operations research, optimization theory, linear algebra, interval analysis, reliable computing, and fuzzy sets. The book will also be useful for researchers in these respective areas Nota de contenido: Matrices -- Solvability of systems of interval linear equations and inequalities -- Interval linear programming -- Linear programming with set coefficients -- Fuzzy linear optimization -- Interval linear systems and optimization problems over max-algebras En línea: http://dx.doi.org/10.1007/0-387-32698-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34797 Ejemplares
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Título : Linear Algebra Tipo de documento: documento electrónico Autores: Peter Petersen ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2012 Otro editor: Imprint: Springer Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: X, 390 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-3612-6 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Linear and Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: This textbook on linear algebra includes the key topics of the subject that most advanced undergraduates need to learn before entering graduate school. All the usual topics, such as complex vector spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form, and the rational canonical form, are covered, along with a chapter on determinants at the end of the book. In addition, there is material throughout the text on linear differential equations and how it integrates with all of the important concepts in linear algebra. This book has several distinguishing features that set it apart from other linear algebra texts. For example: Gaussian elimination is used as the key tool in getting at eigenvalues; it takes an essentially determinant-free approach to linear algebra; and systems of linear differential equations are used as frequent motivation for the reader. Another motivating aspect of the book is the excellent and engaging exercises that abound in this text. This textbook is written for an upper-division undergraduate course on Linear Algebra. The prerequisites for this book are a familiarity with basic matrix algebra and elementary calculus, although any student who is willing to think abstractly should not have too much difficulty in understanding this text Nota de contenido: Preface -- 1 Basic Theory -- 2 Linear Operators -- 3 Inner Product Spaces -- 4 Linear Operators on Inner Product Spaces -- 5 Determinants -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-3612-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32804 Linear Algebra [documento electrónico] / Peter Petersen ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2012 . - X, 390 p : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-1-4614-3612-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Linear and Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: This textbook on linear algebra includes the key topics of the subject that most advanced undergraduates need to learn before entering graduate school. All the usual topics, such as complex vector spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form, and the rational canonical form, are covered, along with a chapter on determinants at the end of the book. In addition, there is material throughout the text on linear differential equations and how it integrates with all of the important concepts in linear algebra. This book has several distinguishing features that set it apart from other linear algebra texts. For example: Gaussian elimination is used as the key tool in getting at eigenvalues; it takes an essentially determinant-free approach to linear algebra; and systems of linear differential equations are used as frequent motivation for the reader. Another motivating aspect of the book is the excellent and engaging exercises that abound in this text. This textbook is written for an upper-division undergraduate course on Linear Algebra. The prerequisites for this book are a familiarity with basic matrix algebra and elementary calculus, although any student who is willing to think abstractly should not have too much difficulty in understanding this text Nota de contenido: Preface -- 1 Basic Theory -- 2 Linear Operators -- 3 Inner Product Spaces -- 4 Linear Operators on Inner Product Spaces -- 5 Determinants -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-3612-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32804 Ejemplares
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Título : Linear Algebra and Geometry Tipo de documento: documento electrónico Autores: Shafarevich, Igor R ; SpringerLink (Online service) ; Alexey O. Remizov Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2013 Otro editor: Imprint: Springer Número de páginas: XXII, 526 p Il.: online resource ISBN/ISSN/DL: 978-3-642-30994-6 Idioma : Inglés (eng) Materias: Álgebra lineal Palabras clave: Mathematics Algebra Associative rings Rings (Algebra) Matrix theory Geometry Linear and Multilinear Algebras, Theory Algebras Clasificación: 512.64 Álgebra lineal y multilineal Resumen: This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics Nota de contenido: Preface -- Preliminaries -- 1. Linear Equations -- 2. Matrices and Determinants -- 3. Vector Spaces -- 4. Linear Transformations of a Vector Space to Itself -- 5. Jordan Normal Form -- 6. Quadratic and Bilinear Forms -- 7. Euclidean Spaces -- 8. Affine Spaces -- 9. Projective Spaces -- 10. The Exterior Product and Exterior Algebras -- 11. Quadrics -- 12. Hyperbolic Geometry -- 13. Groups, Rings, and Modules -- 14. Elements of Representation Theory -- Historical Note -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-642-30994-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32508 Linear Algebra and Geometry [documento electrónico] / Shafarevich, Igor R ; SpringerLink (Online service) ; Alexey O. Remizov . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013 . - XXII, 526 p : online resource.
ISBN : 978-3-642-30994-6
Idioma : Inglés (eng)
Materias: Álgebra lineal Palabras clave: Mathematics Algebra Associative rings Rings (Algebra) Matrix theory Geometry Linear and Multilinear Algebras, Theory Algebras Clasificación: 512.64 Álgebra lineal y multilineal Resumen: This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics Nota de contenido: Preface -- Preliminaries -- 1. Linear Equations -- 2. Matrices and Determinants -- 3. Vector Spaces -- 4. Linear Transformations of a Vector Space to Itself -- 5. Jordan Normal Form -- 6. Quadratic and Bilinear Forms -- 7. Euclidean Spaces -- 8. Affine Spaces -- 9. Projective Spaces -- 10. The Exterior Product and Exterior Algebras -- 11. Quadrics -- 12. Hyperbolic Geometry -- 13. Groups, Rings, and Modules -- 14. Elements of Representation Theory -- Historical Note -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-642-30994-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32508 Ejemplares
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Título : Linear algebra : for everyone Tipo de documento: documento electrónico Autores: Lorenzo Robbiano ; SpringerLink (Online service) Editorial: Milano : Springer Milan Fecha de publicación: 2011 Número de páginas: XVII, 218 p Il.: online resource ISBN/ISSN/DL: 978-88-470-1839-6 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Linear and Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: This book provides students with the rudiments of Linear Algebra, a fundamental subject for students in all areas of science and technology. The book would also be good for statistics students studying linear algebra. It is the translation of a successful textbook currently being used in Italy. The author is a mathematician sensitive to the needs of a general audience. In addition to introducing fundamental ideas in Linear Algebra through a wide variety of interesting examples, the book also discusses topics not usually covered in an elementary text (e.g. the "cost" of operations, generalized inverses, approximate solutions). The challenge is to show why the "everyone" in the title can find Linear Algebra useful and easy to learn. The translation has been prepared by a native English speaking mathematician, Professor Anthony V. Geramita En línea: http://dx.doi.org/10.1007/978-88-470-1839-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33469 Linear algebra : for everyone [documento electrónico] / Lorenzo Robbiano ; SpringerLink (Online service) . - Milano : Springer Milan, 2011 . - XVII, 218 p : online resource.
ISBN : 978-88-470-1839-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Linear and Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: This book provides students with the rudiments of Linear Algebra, a fundamental subject for students in all areas of science and technology. The book would also be good for statistics students studying linear algebra. It is the translation of a successful textbook currently being used in Italy. The author is a mathematician sensitive to the needs of a general audience. In addition to introducing fundamental ideas in Linear Algebra through a wide variety of interesting examples, the book also discusses topics not usually covered in an elementary text (e.g. the "cost" of operations, generalized inverses, approximate solutions). The challenge is to show why the "everyone" in the title can find Linear Algebra useful and easy to learn. The translation has been prepared by a native English speaking mathematician, Professor Anthony V. Geramita En línea: http://dx.doi.org/10.1007/978-88-470-1839-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33469 Ejemplares
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