Linear Algebra Inner Product Spaces
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Linear Algebra Done Right
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Author : Sheldon Axler
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-07-18
Linear Algebra Done Right written by Sheldon Axler 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 1997-07-18 with Mathematics categories.
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.
Linear Algebra
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Author : Werner Hildbert Greub
language : en
Publisher:
Release Date : 1974
Linear Algebra written by Werner Hildbert Greub and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Algebras, Linear categories.
Linear Algebra Inner Product Spaces
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Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :
Linear Algebra Inner Product Spaces written by N.B. Singh and has been published by N.B. Singh this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
"Linear Algebra: Inner Product Spaces" is a comprehensive introductory guide designed for absolute beginners seeking to grasp the fundamental concepts of linear algebra within the context of inner product spaces. This book provides clear explanations and practical examples to facilitate understanding of vectors, matrices, orthogonality, projections, and their applications across diverse fields such as quantum mechanics, signal processing, and machine learning. With an emphasis on accessibility and relevance, it equips readers with essential tools to comprehend and apply linear algebra in solving real-world problems and advancing their mathematical proficiency.
Operator Theory In Inner Product Spaces
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Author : Karl-Heinz Förster
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-20
Operator Theory In Inner Product Spaces written by Karl-Heinz Förster 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 2007-03-20 with Mathematics categories.
This volume contains contributions written by participants of the 4th Workshop on Operator Theory in Krein Spaces and Applications, held at the TU Berlin, Germany, December 17 to 19, 2004. The workshop covered topics from spectral, perturbation, and extension theory of linear operators and relations in inner product spaces.
Best Approximation In Inner Product Spaces
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Author : Frank Deutsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-04-20
Best Approximation In Inner Product Spaces written by Frank Deutsch 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 2001-04-20 with Computers categories.
This book evolved from notes originally developed for a graduate course, "Best Approximation in Normed Linear Spaces," that I began giving at Penn State Uni versity more than 25 years ago. It soon became evident. that many of the students who wanted to take the course (including engineers, computer scientists, and statis ticians, as well as mathematicians) did not have the necessary prerequisites such as a working knowledge of Lp-spaces and some basic functional analysis. (Today such material is typically contained in the first-year graduate course in analysis. ) To accommodate these students, I usually ended up spending nearly half the course on these prerequisites, and the last half was devoted to the "best approximation" part. I did this a few times and determined that it was not satisfactory: Too much time was being spent on the presumed prerequisites. To be able to devote most of the course to "best approximation," I decided to concentrate on the simplest of the normed linear spaces-the inner product spaces-since the theory in inner product spaces can be taught from first principles in much less time, and also since one can give a convincing argument that inner product spaces are the most important of all the normed linear spaces anyway. The success of this approach turned out to be even better than I had originally anticipated: One can develop a fairly complete theory of best approximation in inner product spaces from first principles, and such was my purpose in writing this book.
Indefinite Linear Algebra And Applications
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Author : Israel Gohberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-08
Indefinite Linear Algebra And Applications written by Israel Gohberg 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 2006-02-08 with Mathematics categories.
This book covers recent results in linear algebra with indefinite inner product. It includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications are based on linear algebra in spaces with indefinite inner product. The latter forms an independent branch of linear algebra called indefinite linear algebra. This new subject is presented following the principles of a standard linear algebra course.
Applied Linear Algebra
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Author : Peter J. Olver
language : en
Publisher: Springer
Release Date : 2018-05-30
Applied Linear Algebra written by Peter J. Olver and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-30 with Mathematics categories.
This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the underlying linear algebraic techniques, thereby enabling students not only to learn how to apply the mathematical tools in routine contexts, but also to understand what is required to adapt to unusual or emerging problems. No previous knowledge of linear algebra is needed to approach this text, with single-variable calculus as the only formal prerequisite. However, the reader will need to draw upon some mathematical maturity to engage in the increasing abstraction inherent to the subject. Once equipped with the main tools and concepts from this book, students will be prepared for further study in differential equations, numerical analysis, data science and statistics, and a broad range of applications. The first author’s text, Introduction to Partial Differential Equations, is an ideal companion volume, forming a natural extension of the linear mathematical methods developed here.
Locally Convex Spaces Over Non Archimedean Valued Fields
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Author : C. Perez-Garcia
language : en
Publisher: Cambridge University Press
Release Date : 2010-01-07
Locally Convex Spaces Over Non Archimedean Valued Fields written by C. Perez-Garcia and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-07 with Mathematics categories.
Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research. A guide to the many illustrative examples provided, end-of-chapter notes and glossary of terms all make this book easily accessible to beginners at the graduate level, as well as specialists from a variety of disciplines.
Elementary Linear Algebra
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Author : Stephen Andrilli
language : en
Publisher: Academic Press
Release Date : 2010-02-04
Elementary Linear Algebra written by Stephen Andrilli and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-04 with Mathematics categories.
Elementary Linear Algebra develops and explains in careful detail the computational techniques and fundamental theoretical results central to a first course in linear algebra. This highly acclaimed text focuses on developing the abstract thinking essential for further mathematical study The authors give early, intensive attention to the skills necessary to make students comfortable with mathematical proofs. The text builds a gradual and smooth transition from computational results to general theory of abstract vector spaces. It also provides flexbile coverage of practical applications, exploring a comprehensive range of topics. Ancillary list:* Maple Algorithmic testing- Maple TA- www.maplesoft.com - Includes a wide variety of applications, technology tips and exercises, organized in chart format for easy reference - More than 310 numbered examples in the text at least one for each new concept or application - Exercise sets ordered by increasing difficulty, many with multiple parts for a total of more than 2135 questions - Provides an early introduction to eigenvalues/eigenvectors - A Student solutions manual, containing fully worked out solutions and instructors manual available
Introduction To Applied Linear Algebra
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Author : Stephen Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2018-06-07
Introduction To Applied Linear Algebra written by Stephen Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Business & Economics categories.
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.