A Polynomial Approach To Linear Algebra PDF Download
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| Author | : Paul A. Fuhrmann |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 368 |
| Release | : 2012-10-01 |
| Genre | : Mathematics |
| ISBN | : 1441987347 |
Download A Polynomial Approach to Linear Algebra Book in PDF, ePub and Kindle
A Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to other areas of mathematics, operator theory in particular. This technique is very powerful as becomes clear from the analysis of canonical forms (Frobenius, Jordan). It should be emphasized that these functional methods are not only of great theoretical interest, but lead to computational algorithms. Quadratic forms are treated from the same perspective, with emphasis on the important examples of Bezoutian and Hankel forms. These topics are of great importance in applied areas such as signal processing, numerical linear algebra, and control theory. Stability theory and system theoretic concepts, up to realization theory, are treated as an integral part of linear algebra. Finally there is a chapter on Hankel norm approximation for the case of scalar rational functions which allows the reader to access ideas and results on the frontier of current research.
| Author | : |
| Publisher | : |
| Total Pages | : 428 |
| Release | : 2011-11-23 |
| Genre | : |
| ISBN | : 9781461403395 |
Download A Polynomial Approach to Linear Algebra Book in PDF, ePub and Kindle
| Author | : Fernando Barrera-Mora |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 312 |
| Release | : 2023-05-08 |
| Genre | : Mathematics |
| ISBN | : 3111135918 |
Download Linear Algebra Book in PDF, ePub and Kindle
There are numerous linear algebra textbooks available on the market. Yet, there are few that approach the notion of eigenvectors and eigenvalues across an operator's minimum polynomial. In this book, we take that approach. This book provides a thorough introduction to the fundamental concepts of linear algebra. The material is divided into two sections: Part I covers fundamental concepts in linear algebra, whereas Part II covers the theory of determinants, the theory of eigenvalues and eigenvectors, and fundamental results on Euclidean vector spaces. We highlight that: Consider hypothetical manufacturing models as a starting point for studying linear equations. There are two novel ideas in the book: the use of a production model to motivate the concept of matrix product and the use of an operator's minimal polynomial to describe the theory of eigenvalues and eigenvectors. Several examples incorporate the use of SageMath., allowing the reader to focus on conceptual comprehension rather than formulas.
| Author | : Harold M. Edwards |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 196 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 0817644466 |
Download Linear Algebra Book in PDF, ePub and Kindle
* Proposes a radically new and thoroughly algorithmic approach to linear algebra * Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples * Designed for a one-semester course, this text gives the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject
| Author | : A. Bultheel |
| Publisher | : Elsevier |
| Total Pages | : 465 |
| Release | : 1997-11-17 |
| Genre | : Computers |
| ISBN | : 0080535526 |
Download Linear Algebra, Rational Approximation and Orthogonal Polynomials Book in PDF, ePub and Kindle
Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal Padé tables, look-ahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace methods. It introduces the basics of fast algorithms for structured problems and shows how they deal with singular situations. Links are made with more applied subjects such as linear system theory and signal processing, and with more advanced topics and recent results such as general bi-orthogonal polynomials, minimal Padé approximation, polynomial root location problems in the complex plane, very general rational interpolation problems, and the lifting scheme for wavelet transform computation. The text serves as a supplement to existing books on structured linear algebra problems, rational approximation and orthogonal polynomials. Features of this book: • provides a unifying approach to linear algebra, rational approximation and orthogonal polynomials • requires an elementary knowledge of calculus and linear algebra yet introduces advanced topics. The book will be of interest to applied mathematicians and engineers and to students and researchers.
| Author | : Harvey E. Rose |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 288 |
| Release | : 2002-10-01 |
| Genre | : Mathematics |
| ISBN | : 9783764367923 |
Download Linear Algebra Book in PDF, ePub and Kindle
In algebra, an entity is called linear if it can be expressed in terms of addition, and multiplication by a scalar; a linear expression is a sum of scalar multiples of the entities under consideration. Also, an operation is called linear if it preserves addition, and multiplication by a scalar. For example, if A and Bare 2 x 2 real matrices, v is a (row) vector in the real plane, and c is a real number, then v(A + B) = vA + vB and (cv)A = c(vA), that is, the process of applying a matrix to a vector is linear. Linear Algebra is the study of properties and systems which preserve these two operations, and the following pages present the basic theory and results of this important branch of pure mathematics. There are many books on linear algebra in the bookshops and libraries of the world, so why write another? A number of excellent texts were written about fifty years ago (see the bibliography); in the intervening period the 'style' of math ematical presentation has changed. Also, some of the more modern texts have concentrated on applications both inside and outside mathematics. There is noth ing wrong with this approach; these books serve a very useful purpose. But linear algebra contains some fine pure mathematics and so a modern text taking the pure mathematician's viewpoint was thought to be worthwhile.
| Author | : Vladimír Kučera |
| Publisher | : John Wiley & Sons |
| Total Pages | : 216 |
| Release | : 1979 |
| Genre | : Control theory |
| ISBN | : |
Download Discrete Linear Control Book in PDF, ePub and Kindle
Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.
| Author | : Stephen Boyd |
| Publisher | : Cambridge University Press |
| Total Pages | : 477 |
| Release | : 2018-06-07 |
| Genre | : Business & Economics |
| ISBN | : 1316518965 |
Download Introduction to Applied Linear Algebra Book in PDF, ePub and Kindle
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
| Author | : Sheldon Axler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 276 |
| Release | : 1997-07-18 |
| Genre | : Mathematics |
| ISBN | : 9780387982595 |
Download Linear Algebra Done Right Book in PDF, ePub and Kindle
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
| Author | : Jörg Liesen |
| Publisher | : Springer |
| Total Pages | : 321 |
| Release | : 2015-11-20 |
| Genre | : Mathematics |
| ISBN | : 3319243462 |
Download Linear Algebra Book in PDF, ePub and Kindle
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.
