Download or read book Algebras of Linear Transformations written by Douglas R. Farenick and published by Springer Science & Business Media. This book was released on 2000-10-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies algebras and linear transformations acting on finite-dimensional vector spaces over arbitrary fields. It is written for readers who have prior knowledge of algebra and linear algebra. The goal is to present a balance of theory and example in order for readers to gain a firm understanding of the basic theory of finite-dimensional algebras and to provide a foundation for subsequent advanced study in a number of areas of mathematics.
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.
Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Download or read book Introduction to Linear and Matrix Algebra written by Nathaniel Johnston and published by Springer Nature. This book was released on 2021-05-19 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.
Download or read book Advanced Linear Algebra written by Bruce Cooperstein and published by CRC Press. This book was released on 2016-04-19 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Linear Algebra focuses on vector spaces and the maps between them that preserve their structure (linear transformations). It starts with familiar concepts and then slowly builds to deeper results. Along with including many exercises and examples, each section reviews what students need to know before studying the material. The book first introduces vector spaces over fields as well as the fundamental concepts of linear combinations, span of vectors, linear independence, basis, and dimension. After covering linear transformations, it discusses the algebra of polynomials with coefficients in a field, concentrating on results that are consequences of the division algorithm. The author then develops the whole structure theory of a linear operator on a finite dimensional vector space from a collection of some simple results. He also explores the entire range of topics associated with inner product spaces, from the Gram–Schmidt process to the spectral theorems for normal and self-adjoint operators on an inner product space. The text goes on to rigorously describe the trace and determinant of linear operators and square matrices. The final two chapters focus on bilinear forms and tensor products and related material. Designed for advanced undergraduate and beginning graduate students, this textbook shows students the beauty of linear algebra. It also prepares them for further study in mathematics.
Download or read book Linear Algebra and Geometry written by Igor R. Shafarevich and published by Springer Science & Business Media. This book was released on 2012-08-23 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.
Download or read book Linear Algebra over Commutative Rings written by Bernard R. McDonald and published by CRC Press. This book was released on 2020-11-26 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.
Download or read book Linear Algebra written by Georgi? Evgen?evich Shilov and published by Courier Corporation. This book was released on 1977-06-01 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.
Download or read book Advanced Linear Algebra written by Steven Roman and published by Springer Science & Business Media. This book was released on 2007-12-31 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers a notably broad range of topics, including some topics not generally found in linear algebra books Contains a discussion of the basics of linear algebra
Download or read book Positive Linear Maps of Operator Algebras written by Erling Størmer and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps. The text examines the maps’ positivity properties, as well as their associated linear functionals together with their density operators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of matters relating to positive linear maps, of which a large proportion is relevant and applicable to today’s quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a whole appeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout.
Download or read book Introduction to Non linear Algebra written by Valeri? Valer?evich Dolotin and published by World Scientific. This book was released on 2007 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Literaturverz. S. 267 - 269
Download or read book Basic Matrix Theory written by Leonard E. Fuller and published by Courier Dover Publications. This book was released on 2017-09-13 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This guide to using matrices as a mathematical tool offers a model for procedure rather than an exposition of theory. Detailed examples illustrate the focus on computational methods. 1962 edition.
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 2007-04-05 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book rigorously deals with the abstract theory and, at the same time, devotes considerable space to the numerical and computational aspects of linear algebra. It features a large number of thumbnail portraits of researchers who have contributed to the development of linear algebra as we know it today and also includes over 1,000 exercises, many of which are very challenging. The book can be used as a self-study guide; a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level; or as a reference book.
Download or read book Linear Algebra Through Geometry written by Thomas Banchoff and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space.
Download or read book Linear Algebra written by Lina Oliveira and published by CRC Press. This book was released on 2022-07-08 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Algebra is intended primarily as an undergraduate textbook but is written in such a way that it can also be a valuable resource for independent learning. The narrative of the book takes a matrix approach: the exposition is intertwined with matrices either as the main subject or as tools to explore the theory. Each chapter contains a description of its aims, a summary at the end of the chapter, exercises, and solutions. The reader is carefully guided through the theory and techniques presented which are outlined throughout in "How to..." text boxes. Common mistakes and pitfalls are also pointed out as one goes along. Features Written to be self-contained Ideal as a primary textbook for an undergraduate course in linear algebra Applications of the general theory which are of interest to disciplines outside of mathematics, such as engineering
Download or read book Linear Algebra Via Exterior Products written by Sergei Winitzki and published by Sergei Winitzki. This book was released on 2009-07-30 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative, "wedge") product of vectors. The coordinate-free formalism and the exterior product, while somewhat more abstract, provide a deeper understanding of the classical results in linear algebra. Without cumbersome matrix calculations, this text derives the standard properties of determinants, the Pythagorean formula for multidimensional volumes, the formulas of Jacobi and Liouville, the Cayley-Hamilton theorem, the Jordan canonical form, the properties of Pfaffians, as well as some generalizations of these results.
Download or read book Indefinite Linear Algebra and Applications written by Israel Gohberg and published by Springer Science & Business Media. This book was released on 2006-02-08 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
