Problems And Theorems In Linear Algebra

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Problems and Theorems in Linear Algebra

Author : Viktor Vasil_evich Prasolov
Publisher : American Mathematical Soc.
ISBN 13 : 0821802364
Total Pages : 250 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Problems and Theorems in Linear Algebra by : Viktor Vasil_evich Prasolov

Download or read book Problems and Theorems in Linear Algebra written by Viktor Vasil_evich Prasolov and published by American Mathematical Soc.. This book was released on 1994-06-13 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are a number of very good books available on linear algebra. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many of these results and proofs obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In this book, the author provides the basics of linear algebra, with an emphasis on new results and on nonstandard and interesting proofs. The book features about 230 problems with complete solutions. It can serve as a supplementary text for an undergraduate or graduate algebra course.

Linear Algebra Problem Book

Author : Paul R. Halmos
Publisher : American Mathematical Soc.
ISBN 13 : 1614442126
Total Pages : 333 pages
Book Rating : 4.6/5 (144 download)

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Book Synopsis Linear Algebra Problem Book by : Paul R. Halmos

Download or read book Linear Algebra Problem Book written by Paul R. Halmos and published by American Mathematical Soc.. This book was released on 1995-12-31 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebraand today that means every user of mathematics. It can be used as the basis of either an official course or a program of private study. If used as a course, the book can stand by itself, or if so desired, it can be stirred in with a standard linear algebra course as the seasoning that provides the interest, the challenge, and the motivation that is needed by experienced scholars as much as by beginning students. The best way to learn is to do, and the purpose of this book is to get the reader to DO linear algebra. The approach is Socratic: first ask a question, then give a hint (if necessary), then, finally, for security and completeness, provide the detailed answer.

Problems and Theorems in Linear Algebra

Author : V. V. Prasolov
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (933 download)

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Book Synopsis Problems and Theorems in Linear Algebra by : V. V. Prasolov

Download or read book Problems and Theorems in Linear Algebra written by V. V. Prasolov and published by . This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Theorems and Problems in Functional Analysis

Author : A. A. Kirillov
Publisher : Springer Science & Business Media
ISBN 13 : 1461381533
Total Pages : 351 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Theorems and Problems in Functional Analysis by : A. A. Kirillov

Download or read book Theorems and Problems in Functional Analysis written by A. A. Kirillov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Even the simplest mathematical abstraction of the phenomena of reality the real line-can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathe matical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures.

Exercises And Problems In Linear Algebra

Author : John M Erdman
Publisher : World Scientific
ISBN 13 : 9811220425
Total Pages : 220 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Exercises And Problems In Linear Algebra by : John M Erdman

Download or read book Exercises And Problems In Linear Algebra written by John M Erdman and published by World Scientific. This book was released on 2020-09-28 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an extensive collection of exercises and problems that address relevant topics in linear algebra. Topics that the author finds missing or inadequately covered in most existing books are also included. The exercises will be both interesting and helpful to an average student. Some are fairly routine calculations, while others require serious thought.The format of the questions makes them suitable for teachers to use in quizzes and assigned homework. Some of the problems may provide excellent topics for presentation and discussions. Furthermore, answers are given for all odd-numbered exercises which will be extremely useful for self-directed learners. In each chapter, there is a short background section which includes important definitions and statements of theorems to provide context for the following exercises and problems.

Problems and Proofs in Numbers and Algebra

Author : Richard S. Millman
Publisher : Springer
ISBN 13 : 3319144278
Total Pages : 223 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Problems and Proofs in Numbers and Algebra by : Richard S. Millman

Download or read book Problems and Proofs in Numbers and Algebra written by Richard S. Millman and published by Springer. This book was released on 2015-02-09 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. The benefit to readers who are moving from calculus to more abstract mathematics is to acquire the ability to understand proofs through use of the book and the multitude of proofs and problems that will be covered throughout. This book is meant to be a transitional precursor to more complex topics in analysis, advanced number theory, and abstract algebra. To achieve the goal of conceptual understanding, a large number of problems and examples will be interspersed through every chapter. The problems are always presented in a multi-step and often very challenging, requiring the reader to think about proofs, counter-examples, and conjectures. Beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high-achieving high school students. Furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathematical knowledge. In the past, PNA has been taught in a "problem solving in middle school” course (twice), to a quite advanced high school students course (three semesters), and three times as a secondary resource for a course for future high school teachers. PNA is suitable for secondary math teachers who look for material to encourage and motivate more high achieving students.

Linear Algebra

Author : Hassan Yasser
Publisher : BoD – Books on Demand
ISBN 13 : 9535106694
Total Pages : 265 pages
Book Rating : 4.5/5 (351 download)

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Book Synopsis Linear Algebra by : Hassan Yasser

Download or read book Linear Algebra written by Hassan Yasser and published by BoD – Books on Demand. This book was released on 2012-07-11 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra occupies a central place in modern mathematics. Also, it is a beautiful and mature field of mathematics, and mathematicians have developed highly effective methods for solving its problems. It is a subject well worth studying for its own sake. This book contains selected topics in linear algebra, which represent the recent contributions in the most famous and widely problems. It includes a wide range of theorems and applications in different branches of linear algebra, such as linear systems, matrices, operators, inequalities, etc. It continues to be a definitive resource for researchers, scientists and graduate students.

Problems in Linear Algebra

Author : I. V. Proskuryakov
Publisher :
ISBN 13 :
Total Pages : 453 pages
Book Rating : 4.:/5 (861 download)

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Book Synopsis Problems in Linear Algebra by : I. V. Proskuryakov

Download or read book Problems in Linear Algebra written by I. V. Proskuryakov and published by . This book was released on 1989 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Linear Algebra in Action

Author : Harry Dym
Publisher : American Mathematical Society
ISBN 13 : 1470472066
Total Pages : 512 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Linear Algebra in Action by : Harry Dym

Download or read book Linear Algebra in Action written by Harry Dym and published by American Mathematical Society. This book was released on 2023-07-18 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based largely on courses that the author taught at the Feinberg Graduate School of the Weizmann Institute. It conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that the author has found to be useful in his own research and wishes that he had been exposed to as a graduate student. Roughly the first quarter of the book reviews the contents of a basic course in linear algebra, plus a little. The remaining chapters treat singular value decompositions, convexity, special classes of matrices, projections, assorted algorithms, and a number of applications. The applications are drawn from vector calculus, numerical analysis, control theory, complex analysis, convex optimization, and functional analysis. In particular, fixed point theorems, extremal problems, best approximations, matrix equations, zero location and eigenvalue location problems, matrices with nonnegative entries, and reproducing kernels are discussed. This new edition differs significantly from the second edition in both content and style. It includes a number of topics that did not appear in the earlier edition and excludes some that did. Moreover, most of the material that has been adapted from the earlier edition has been extensively rewritten and reorganized.

Linear Algebra: Theory and Applications

Author : Kenneth Kuttler
Publisher : The Saylor Foundation
ISBN 13 :
Total Pages : 503 pages
Book Rating : 4./5 ( download)

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Book Synopsis Linear Algebra: Theory and Applications by : Kenneth Kuttler

Download or read book Linear Algebra: Theory and Applications written by Kenneth Kuttler and published by The Saylor Foundation. This book was released on 2012-01-29 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. I think that the subject of linear algebra is likely the most significant topic discussed in undergraduate mathematics courses. Part of the reason for this is its usefulness in unifying so many different topics. Linear algebra is essential in analysis, applied math, and even in theoretical mathematics. This is the point of view of this book, more than a presentation of linear algebra for its own sake. This is why there are numerous applications, some fairly unusual.

The Linear Algebra a Beginning Graduate Student Ought to Know

Author : Jonathan S. Golan
Publisher : Springer Science & Business Media
ISBN 13 : 9400726368
Total Pages : 499 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis The Linear Algebra a Beginning Graduate Student Ought to Know by : Jonathan S. Golan

Download or read book The Linear Algebra a Beginning Graduate Student Ought to Know written by Jonathan S. Golan and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as to computer science, to the physical, biological, and social sciences, and to engineering. It encompasses an extensive corpus of theoretical results as well as a large and rapidly-growing body of computational techniques. Unfortunately, in the past decade, the content of linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or computational background. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the mathematics of the numerical algorithms they need for applications. Certainly, the material presented in the average undergraduate course is insufficient for graduate study. This book is intended to fill the gap which has developed by providing enough theoretical and computational material to allow the advanced undergraduate or beginning graduate student to overcome this deficiency and be able to work independently or in advanced courses. The book is intended to be used either as a self-study guide, a textbook for a course in advanced linear algebra, or as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some of the basic ideas and techniques, such as manipulation of small matrices and the solution of small systems of linear equations over the real numbers. More importantly, it assumes a seriousness of purpose, considerable motivation, and a modicum of mathematical sophistication on the part of the reader. In the latest edition, new major theorems have been added, as well as many new examples. There are over 130 additional exercises and many of the previous exercises have been revised or rewritten. In addition, a large number of additional biographical notes and thumbnail portraits of mathematicians have been included.

Linear Algebra Problem Book

Author : Paul R. Halmos
Publisher : MAA
ISBN 13 : 9780883853221
Total Pages : 354 pages
Book Rating : 4.8/5 (532 download)

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Book Synopsis Linear Algebra Problem Book by : Paul R. Halmos

Download or read book Linear Algebra Problem Book written by Paul R. Halmos and published by MAA. This book was released on 1995 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Takes the student step by step from basic axioms to advanced concepts. 164 problems, each with hints and full solutions.

Linear Algebra and Projective Geometry

Author : Reinhold Baer
Publisher : Courier Corporation
ISBN 13 : 0486154661
Total Pages : 338 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Linear Algebra and Projective Geometry by : Reinhold Baer

Download or read book Linear Algebra and Projective Geometry written by Reinhold Baer and published by Courier Corporation. This book was released on 2012-06-11 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.

Linear Algebra as an Introduction to Abstract Mathematics

Author : Isaiah Lankham
Publisher : World Scientific Publishing Company
ISBN 13 : 9814723797
Total Pages : 208 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Linear Algebra as an Introduction to Abstract Mathematics by : Isaiah Lankham

Download or read book Linear Algebra as an Introduction to Abstract Mathematics written by Isaiah Lankham and published by World Scientific Publishing Company. This book was released on 2015-11-30 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.

Linear Algebra in Action

Author : Harry Dym
Publisher : American Mathematical Soc.
ISBN 13 : 1470409089
Total Pages : 610 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Linear Algebra in Action by : Harry Dym

Download or read book Linear Algebra in Action written by Harry Dym and published by American Mathematical Soc.. This book was released on 2013-12-31 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra permeates mathematics, perhaps more so than any other single subject. It plays an essential role in pure and applied mathematics, statistics, computer science, and many aspects of physics and engineering. This book conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that many of us wish we had been taught as graduate students. Roughly the first third of the book covers the basic material of a first course in linear algebra. The remaining chapters are devoted to applications drawn from vector calculus, numerical analysis, control theory, complex analysis, convexity and functional analysis. In particular, fixed point theorems, extremal problems, matrix equations, zero location and eigenvalue location problems, and matrices with nonnegative entries are discussed. Appendices on useful facts from analysis and supplementary information from complex function theory are also provided for the convenience of the reader. In this new edition, most of the chapters in the first edition have been revised, some extensively. The revisions include changes in a number of proofs, either to simplify the argument, to make the logic clearer or, on occasion, to sharpen the result. New introductory sections on linear programming, extreme points for polyhedra and a Nevanlinna-Pick interpolation problem have been added, as have some very short introductory sections on the mathematics behind Google, Drazin inverses, band inverses and applications of SVD together with a number of new exercises.

Problems in Abstract Algebra

Author : A. R. Wadsworth
Publisher : American Mathematical Soc.
ISBN 13 : 1470435837
Total Pages : 277 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Problems in Abstract Algebra by : A. R. Wadsworth

Download or read book Problems in Abstract Algebra written by A. R. Wadsworth and published by American Mathematical Soc.. This book was released on 2017-05-10 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.

Linear Algebra Done Right

Author : Sheldon Axler
Publisher : Springer Science & Business Media
ISBN 13 : 9780387982595
Total Pages : 276 pages
Book Rating : 4.9/5 (825 download)

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Book Synopsis Linear Algebra Done Right by : Sheldon Axler

Download or read book Linear Algebra Done Right written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 1997-07-18 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.