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| Author | : Steven Roman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 488 |
| Release | : 2007-12-31 |
| Genre | : Mathematics |
| ISBN | : 038727474X |
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
| Author | : Bruce Cooperstein |
| Publisher | : Chapman and Hall/CRC |
| Total Pages | : 622 |
| Release | : 2015-05-13 |
| Genre | : Mathematics |
| ISBN | : 9781482248845 |
Advanced Linear Algebra, Second Edition takes a gentle approach that starts with familiar concepts and then gradually builds to deeper results. Each section begins with an outline of previously introduced concepts and results necessary for mastering the new material. By reviewing what students need to know before moving forward, the text builds a solid foundation upon which to progress. The new edition of this successful text focuses on vector spaces and the maps between them that preserve their structure (linear transformations). Designed for advanced undergraduate and beginning graduate students, the book discusses the structure theory of an operator, various topics on inner product spaces, and the trace and determinant functions of a linear operator. It addresses bilinear forms with a full treatment of symplectic spaces and orthogonal spaces, as well as explains the construction of tensor, symmetric, and exterior algebras. Featuring updates and revisions throughout, Advanced Linear Algebra, Second Edition: Contains new chapters covering sesquilinear forms, linear groups and groups of isometries, matrices, and three important applications of linear algebra Adds sections on normed vector spaces, orthogonal spaces over perfect fields of characteristic two, and Clifford algebras Includes several new exercises and examples, with a solutions manual available upon qualifying course adoption The book shows students the beauty of linear algebra while preparing them for further study in mathematics.
| Author | : Steven Roman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 528 |
| Release | : 2007-09-20 |
| Genre | : Mathematics |
| ISBN | : 0387728317 |
This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems.
| Author | : Nathaniel Johnston |
| Publisher | : Springer Nature |
| Total Pages | : 482 |
| Release | : 2021-05-19 |
| Genre | : Mathematics |
| ISBN | : 3030528111 |
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.
| Author | : Hugo Woerdeman |
| Publisher | : CRC Press |
| Total Pages | : 348 |
| Release | : 2015-12-23 |
| Genre | : Mathematics |
| ISBN | : 149875404X |
Advanced Linear Algebra features a student-friendly approach to the theory of linear algebra. The author’s emphasis on vector spaces over general fields, with corresponding current applications, sets the book apart. He focuses on finite fields and complex numbers, and discusses matrix algebra over these fields. The text then proceeds to cover vector spaces in depth. Also discussed are standard topics in linear algebra including linear transformations, Jordan canonical form, inner product spaces, spectral theory, and, as supplementary topics, dual spaces, quotient spaces, and tensor products. Written in clear and concise language, the text sticks to the development of linear algebra without excessively addressing applications. A unique chapter on "How to Use Linear Algebra" is offered after the theory is presented. In addition, students are given pointers on how to start a research project. The proofs are clear and complete and the exercises are well designed. In addition, full solutions are included for almost all exercises.
| Author | : Nicholas Loehr |
| Publisher | : CRC Press |
| Total Pages | : 619 |
| Release | : 2014-04-10 |
| Genre | : Mathematics |
| ISBN | : 1466559020 |
Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs. It explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra,
| Author | : Yisong Yang |
| Publisher | : Cambridge University Press |
| Total Pages | : 333 |
| Release | : 2015 |
| Genre | : Mathematics |
| ISBN | : 1107087511 |
This engaging, well-motivated textbook helps advanced undergraduate students to grasp core concepts and reveals applications in mathematics and beyond.
| Author | : Sohail A. Dianat |
| Publisher | : CRC Press |
| Total Pages | : 346 |
| Release | : 2017-12-19 |
| Genre | : Mathematics |
| ISBN | : 1420095242 |
Arming readers with both theoretical and practical knowledge, Advanced Linear Algebra for Engineers with MATLAB® provides real-life problems that readers can use to model and solve engineering and scientific problems in fields ranging from signal processing and communications to electromagnetics and social and health sciences. Facilitating a unique understanding of rapidly evolving linear algebra and matrix methods, this book: Outlines the basic concepts and definitions behind matrices, matrix algebra, elementary matrix operations, and matrix partitions, describing their potential use in signal and image processing applications Introduces concepts of determinants, inverses, and their use in solving linear equations that result from electrical and mechanical-type systems Presents special matrices, linear vector spaces, and fundamental principles of orthogonality, using an appropriate blend of abstract and concrete examples and then discussing associated applications to enhance readers’ visualization of presented concepts Discusses linear operators, eigenvalues, and eigenvectors, and explores their use in matrix diagonalization and singular value decomposition Extends presented concepts to define matrix polynomials and compute functions using several well-known methods, such as Sylvester’s expansion and Cayley-Hamilton Introduces state space analysis and modeling techniques for discrete and continuous linear systems, and explores applications in control and electromechanical systems, to provide a complete solution for the state space equation Shows readers how to solve engineering problems using least square, weighted least square, and total least square techniques Offers a rich selection of exercises and MATLAB® assignments that build a platform to enhance readers’ understanding of the material Striking the appropriate balance between theory and real-life applications, this book provides both advanced students and professionals in the field with a valuable reference that they will continually consult.
| Author | : Bruce Cooperstein |
| Publisher | : CRC Press |
| Total Pages | : 361 |
| Release | : 2016-04-19 |
| Genre | : Mathematics |
| ISBN | : 1439829691 |
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.
| Author | : Stephan Ramon Garcia |
| Publisher | : Cambridge University Press |
| Total Pages | : 447 |
| Release | : 2017-05-11 |
| Genre | : Mathematics |
| ISBN | : 1107103819 |
A second course in linear algebra for undergraduates in mathematics, computer science, physics, statistics, and the biological sciences.
