Linear Dependence
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Linear Dependence
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Author : Sydney N. Afriat
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear Dependence written by Sydney N. Afriat and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Deals with the most basic notion of linear algebra, to bring emphasis on approaches to the topic serving at the elementary level and more broadly. A typical feature is where computational algorithms and theoretical proofs are brought together. Another is respect for symmetry, so that when this has some part in the form of a matter it should also be reflected in the treatment. Issues relating to computational method are covered. These interests may have suggested a limited account, to be rounded-out suitably. However this limitation where basic material is separated from further reaches of the subject has an appeal of its own. To the `elementary operations' method of the textbooks for doing linear algebra, Albert Tucker added a method with his `pivot operation'. Here there is a more primitive method based on the `linear dependence table', and yet another based on `rank reduction'. The determinant is introduced in a completely unusual upside-down fashion where Cramer's rule comes first. Also dealt with is what is believed to be a completely new idea, of the `alternant', a function associated with the affine space the way the determinant is with the linear space, with n+1 vector arguments, as the determinant has n. Then for affine (or barycentric) coordinates we find a rule which is an unprecedented exact counterpart of Cramer's rule for linear coordinates, where the alternant takes on the role of the determinant. These are among the more distinct or spectacular items for possible novelty, or unfamiliarity. Others, with or without some remark, may be found scattered in different places.
The Theory Of Linear Dependence
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Author : Maxime Bôcher
language : en
Publisher:
Release Date : 1901
The Theory Of Linear Dependence written by Maxime Bôcher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1901 with Differential equations, Linear categories.
Linear Algebra Thoroughly Explained
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Author : Milan Vujicic
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-16
Linear Algebra Thoroughly Explained written by Milan Vujicic and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-16 with Science categories.
Milan Vujicic was Professor of Theoretical Physics at the University of Belgrade and the book is based on lectures he gave there to both undergraduate and postgraduate students over a period of several decades. He also lectured on the applications of linear algebra in particle physics at the University of Adelaide and, after retirement, taught the subject at the most basic level to Teaching Diploma students at the University of Malta. It was his success in this most recent endeavour that inspired him to write this book which sets out to explain Linear Algebra from its fundamentals to the most advanced level where he, himself, used it throughout his career to solve problems involving linear and anti-linear correlations and symmetries in quantum mechanical applications. Linear Algebra is one of the most important topics in mathematics, of interest in its own right to mathematicians, but also as an enormously powerful tool in the applied sciences, particularly in physics and engineering. A special feature of this book is its didactical approach, with a myriad of thoroughly worked examples and excellent illustrations, which allows the reader to approach the subject from any level and to proceed to that of the most advanced applications. Throughout, the subject is taught with painstaking care.
Advanced Mathematical Methods For Scientists And Engineers I
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Author : Carl M. Bender
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-10-29
Advanced Mathematical Methods For Scientists And Engineers I written by Carl M. Bender and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-29 with Mathematics categories.
A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
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Author : Gareth Williams
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2007-08-17
written by Gareth Williams and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-17 with categories.
Linear Algebra with Applications, Sixth Edition is designed for the introductory course in linear algebra typically offered at the sophomore level. The new Sixth Edition is reorganized and arranged into three important parts. Part 1 introduces the basics, presenting the systems of linear equations, vectors in Rn, matrices, linear transformations, and determinants. Part 2 builds on this material to discuss general vector spaces, such as spaces of matrices and functions. Part 3 completes the course with many of the important ideas and methods in Numerical Linear Algebra, such as ill-conditioning, pivoting, and the LU decomposition. New applications include the role of linear algebra in the operation of the search engine Google and the global structure of the worldwide air transportation network have been added as a means of presenting real-world scenarios of the many functions of linear algebra in modern technology. Clear, Concise, Comprehensive - Linear Algebra with Applications, Sixth Edition continues to educate and enlighten students, providing a broad exposure to the many facets of the field.
Elements Of Linear Algebra
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Author : P.M. Cohn
language : en
Publisher: Routledge
Release Date : 2017-10-19
Elements Of Linear Algebra written by P.M. Cohn and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
This volume presents a thorough discussion of systems of linear equations and their solutions. Vectors and matrices are introduced as required and an account of determinants is given. Great emphasis has been placed on keeping the presentation as simple as possible, with many illustrative examples. While all mathematical assertions are proved, the student is led to view the mathematical content intuitively, as an aid to understanding.The text treats the coordinate geometry of lines, planes and quadrics, provides a natural application for linear algebra and at the same time furnished a geometrical interpretation to illustrate the algebraic concepts.
An Introduction To Multivariable Mathematics
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Author : Leon Simon
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2008
An Introduction To Multivariable Mathematics written by Leon Simon and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The core material of this text is arranged to allow for the main introductory material on linear algebra, including basic vector space theory in Euclidean space and the initial theory of matrices and linear systems, to be covered in ten or eleven lectures, followed by a similar number of lectures on basic multivariable analysis, including first theorems on differentiable functions on domains in Euclidean space and a brief introduction to submanifolds.
The Linear Algebra Survival Guide
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Author : Fred Szabo
language : en
Publisher: Academic Press
Release Date : 2015-02-27
The Linear Algebra Survival Guide written by Fred Szabo and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-27 with Mathematics categories.
The Linear Algebra Survival Guide offers a concise introduction to the difficult core topics of linear algebra, guiding you through the powerful graphic displays and visualization of Mathematica that make the most abstract theories seem simple - allowing you to tackle realistic problems using simple mathematical manipulations. This resource is therefore a guide to learning the content of Mathematica in a practical way, enabling you to manipulate potential solutions/outcomes, and learn creatively. No starting knowledge of the Mathematica system is required to use the book. Desktop, laptop, web-based versions of Mathematica are available on all major platforms. Mathematica Online for tablet and smartphone systems are also under development and increases the reach of the guide as a general reference, teaching and learning tool. - Includes computational oriented information that complements the essential topics in linear algebra. - Presents core topics in a simple, straightforward way with examples for exploring computational illustrations, graphics, and displays using Mathematica. - Provides numerous examples of short code in the text, which can be modified for use with exercises to develop graphics displays for teaching, learning, and demonstrations.
Modeling Dependence In Econometrics
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Author : Van-Nam Huynh
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-18
Modeling Dependence In Econometrics written by Van-Nam Huynh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-18 with Technology & Engineering categories.
In economics, many quantities are related to each other. Such economic relations are often much more complex than relations in science and engineering, where some quantities are independence and the relation between others can be well approximated by linear functions. As a result of this complexity, when we apply traditional statistical techniques - developed for science and engineering - to process economic data, the inadequate treatment of dependence leads to misleading models and erroneous predictions. Some economists even blamed such inadequate treatment of dependence for the 2008 financial crisis. To make economic models more adequate, we need more accurate techniques for describing dependence. Such techniques are currently being developed. This book contains description of state-of-the-art techniques for modeling dependence and economic applications of these techniques. Most of these research developments are centered around the notion of a copula - a general way of describing dependence in probability theory and statistics. To be even more adequate, many papers go beyond traditional copula techniques and take into account, e.g., the dynamical (changing) character of the dependence in economics.
Linear Algebra
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Author :
language : en
Publisher: Ardent Media
Release Date :
Linear Algebra written by and has been published by Ardent Media this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.