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Author: Yitzhak Katznelson
Publisher: American Mathematical Soc.
Published: 2008
Total Pages: 234
ISBN-13: 0821844199
DOWNLOAD EBOOKLinear algebra is the study of vector spaces and the linear maps between them. It underlies much of modern mathematics and is widely used in applications.
Author: Serge Lang
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 300
ISBN-13: 1461210704
DOWNLOAD EBOOKThis is a short text in linear algebra, intended for a one-term course. In the first chapter, Lang discusses the relation between the geometry and the algebra underlying the subject, and gives concrete examples of the notions which appear later in the book. He then starts with a discussion of linear equations, matrices and Gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, while others are conceptual.
Author: Sheldon Axler
Publisher: Springer Science & Business Media
Published: 1997-07-18
Total Pages: 276
ISBN-13: 9780387982595
DOWNLOAD EBOOKThis 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: John M. Franks
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 219
ISBN-13: 0821848623
DOWNLOAD EBOOKProvides a student's first encounter with the concepts of measure theory and functional analysis. This book reflects the belief that difficult concepts should be introduced in their simplest and most concrete forms. It is suitable for an advanced undergraduate course or for the start of a graduate course.
Author: Thomas S. Shores
Publisher: Springer Science & Business Media
Published: 2007-03-12
Total Pages: 394
ISBN-13: 0387489479
DOWNLOAD EBOOKThis new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises.
Author: Gilbert Strang
Publisher: Wellesley College
Published: 1993
Total Pages: 488
ISBN-13:
DOWNLOAD EBOOKBook Description: Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'. Introduction to Linear Algebra, Fourth Edition includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course is followed by seven applications: differential equations, engineering, graph theory, statistics, Fourier methods and the FFT, linear programming, and computer graphics. Thousands of teachers in colleges and universities and now high schools are using this book, which truly explains this crucial subject.
Author: Bruno Nachtergaele
Publisher: World Scientific Publishing Company
Published: 2015-11-30
Total Pages: 209
ISBN-13: 9814723797
DOWNLOAD EBOOKThis 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.
Author: Gerardo Chacón
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2016-12-19
Total Pages: 298
ISBN-13: 3110433648
DOWNLOAD EBOOKThis textbook on functional analysis offers a short and concise introduction to the subject. The book is designed in such a way as to provide a smooth transition between elementary and advanced topics and its modular structure allows for an easy assimilation of the content. Starting from a dedicated chapter on the axiom of choice, subsequent chapters cover Hilbert spaces, linear operators, functionals and duality, Fourier series, Fourier transform, the fixed point theorem, Baire categories, the uniform bounded principle, the open mapping theorem, the closed graph theorem, the Hahn–Banach theorem, adjoint operators, weak topologies and reflexivity, operators in Hilbert spaces, spectral theory of operators in Hilbert spaces, and compactness. Each chapter ends with workable problems. The book is suitable for graduate students, but also for advanced undergraduates, in mathematics and physics. Contents: List of Figures Basic Notation Choice Principles Hilbert Spaces Completeness, Completion and Dimension Linear Operators Functionals and Dual Spaces Fourier Series Fourier Transform Fixed Point Theorem Baire Category Theorem Uniform Boundedness Principle Open Mapping Theorem Closed Graph Theorem Hahn–Banach Theorem The Adjoint Operator Weak Topologies and Reflexivity Operators in Hilbert Spaces Spectral Theory of Operators on Hilbert Spaces Compactness Bibliography Index
Author: Michael Spivak
Publisher: Westview Press
Published: 1965
Total Pages: 164
ISBN-13: 9780805390216
DOWNLOAD EBOOKThis book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.
Author: Joseph Landin
Publisher: Courier Corporation
Published: 2012-08-29
Total Pages: 275
ISBN-13: 0486150410
DOWNLOAD EBOOKThis self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.
