Linear Algebra Core Topics For The Second Course
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Author |
: Helene Shapiro |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 338 |
Release |
: 2015-10-08 |
ISBN-10 |
: 9781470418526 |
ISBN-13 |
: 1470418525 |
Rating |
: 4/5 (26 Downloads) |
Synopsis Linear Algebra and Matrices by : Helene Shapiro
Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems. Notable features include a discussion of the Weyr characteristic and Weyr canonical forms, and their relationship to the better-known Jordan canonical form; the use of block cyclic matrices and directed graphs to prove Frobenius's theorem on the structure of the eigenvalues of a nonnegative, irreducible matrix; and the inclusion of such combinatorial topics as BIBDs, Hadamard matrices, and strongly regular graphs. Also included are McCoy's theorem about matrices with property P, the Bruck-Ryser-Chowla theorem on the existence of block designs, and an introduction to Markov chains. This book is intended for those who are familiar with the linear algebra covered in a typical first course and are interested in learning more advanced results.
Author |
: Dragu Atanasiu |
Publisher |
: World Scientific |
Total Pages |
: 465 |
Release |
: 2020-03-26 |
ISBN-10 |
: 9789811215049 |
ISBN-13 |
: 9811215049 |
Rating |
: 4/5 (49 Downloads) |
Synopsis Linear Algebra: Core Topics For The First Course by : Dragu Atanasiu
The book is an introduction to linear algebra intended as a textbook for the first course in linear algebra. In the first six chapters we present the core topics: matrices, the vector space ℝn, orthogonality in ℝn, determinants, eigenvalues and eigenvectors, and linear transformations. The book gives students an opportunity to better understand linear algebra in the next three chapters: Jordan forms by examples, singular value decomposition, and quadratic forms and positive definite matrices.In the first nine chapters everything is formulated in terms of ℝn. This makes the ideas of linear algebra easier to understand. The general vector spaces are introduced in Chapter 10. The last chapter presents problems solved with a computer algebra system. At the end of the book we have results or solutions for odd numbered exercises.
Author |
: Dragu Atanasiu |
Publisher |
: World Scientific |
Total Pages |
: 333 |
Release |
: 2023-01-04 |
ISBN-10 |
: 9789811258565 |
ISBN-13 |
: 9811258562 |
Rating |
: 4/5 (65 Downloads) |
Synopsis Linear Algebra: Core Topics For The Second Course by : Dragu Atanasiu
This is a book for the second course in linear algebra whereby students are assumed to be familiar with calculations using real matrices. To facilitate a smooth transition into rigorous proofs, it combines abstract theory with matrix calculations.This book presents numerous examples and proofs of particular cases of important results before the general versions are formulated and proved. The knowledge gained from a particular case, that encapsulates the main idea of a general theorem, can be easily extended to prove another particular case or a general case. For some theorems, there are two or even three proofs provided. In this way, students stand to gain and study important results from different angles and, at the same time, see connections between different results presented in the book.
Author |
: Stephan Ramon Garcia |
Publisher |
: Cambridge University Press |
Total Pages |
: 447 |
Release |
: 2017-05-11 |
ISBN-10 |
: 9781107103818 |
ISBN-13 |
: 1107103819 |
Rating |
: 4/5 (18 Downloads) |
Synopsis A Second Course in Linear Algebra by : Stephan Ramon Garcia
A second course in linear algebra for undergraduates in mathematics, computer science, physics, statistics, and the biological sciences.
Author |
: Irving Kaplansky |
Publisher |
: Courier Corporation |
Total Pages |
: 182 |
Release |
: 2003-01-01 |
ISBN-10 |
: 0486432335 |
ISBN-13 |
: 9780486432335 |
Rating |
: 4/5 (35 Downloads) |
Synopsis Linear Algebra and Geometry by : Irving Kaplansky
The author of this text seeks to remedy a common failing in teaching algebra: the neglect of related instruction in geometry. Focusing on inner product spaces, orthogonal similarity, and elements of geometry, this volume is illustrated with an abundance of examples, exercises, and proofs and is suitable for both undergraduate and graduate courses. 1974 edition.
Author |
: William Clough Brown |
Publisher |
: Wiley-Interscience |
Total Pages |
: 298 |
Release |
: 1988 |
ISBN-10 |
: UVA:X001401506 |
ISBN-13 |
: |
Rating |
: 4/5 (06 Downloads) |
Synopsis A Second Course in Linear Algebra by : William Clough Brown
This textbook for senior undergraduate and first year graduate-level courses in linear algebra and analysis, covers linear algebra, multilinear algebra, canonical forms of matrices, normal linear vector spaces and inner product spaces. These topics provide all of the prerequisites for graduate students in mathematics to prepare for advanced-level work in such areas as algebra, analysis, topology and applied mathematics.
Author |
: Robert J. Valenza |
Publisher |
: Springer |
Total Pages |
: 237 |
Release |
: 1999-02-01 |
ISBN-10 |
: 9780387940991 |
ISBN-13 |
: 0387940995 |
Rating |
: 4/5 (91 Downloads) |
Synopsis Linear Algebra by : Robert J. Valenza
Based on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.
Author |
: Sheldon Axler |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 276 |
Release |
: 1997-07-18 |
ISBN-10 |
: 0387982590 |
ISBN-13 |
: 9780387982595 |
Rating |
: 4/5 (90 Downloads) |
Synopsis Linear Algebra Done Right by : Sheldon Axler
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.
Author |
: Nathaniel Johnston |
Publisher |
: Springer Nature |
Total Pages |
: 482 |
Release |
: 2021-05-19 |
ISBN-10 |
: 9783030528119 |
ISBN-13 |
: 3030528111 |
Rating |
: 4/5 (19 Downloads) |
Synopsis Introduction to Linear and Matrix Algebra by : Nathaniel Johnston
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 |
: Stephan Ramon Garcia |
Publisher |
: Cambridge University Press |
Total Pages |
: 450 |
Release |
: 2017-05-11 |
ISBN-10 |
: 9781108210508 |
ISBN-13 |
: 1108210503 |
Rating |
: 4/5 (08 Downloads) |
Synopsis A Second Course in Linear Algebra by : Stephan Ramon Garcia
Linear algebra is a fundamental tool in many fields, including mathematics and statistics, computer science, economics, and the physical and biological sciences. This undergraduate textbook offers a complete second course in linear algebra, tailored to help students transition from basic theory to advanced topics and applications. Concise chapters promote a focused progression through essential ideas, and contain many examples and illustrative graphics. In addition, each chapter contains a bullet list summarising important concepts, and the book includes over 600 exercises to aid the reader's understanding. Topics are derived and discussed in detail, including the singular value decomposition, the Jordan canonical form, the spectral theorem, the QR factorization, normal matrices, Hermitian matrices (of interest to physics students), and positive definite matrices (of interest to statistics students).