Linear Algebra Core Topics For The First Course

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Linear Algebra: Core Topics For The First Course

Author : Dragu Atanasiu
Publisher : World Scientific
ISBN 13 : 9811215049
Total Pages : 465 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Linear Algebra: Core Topics For The First Course by : Dragu Atanasiu

Download or read book Linear Algebra: Core Topics For The First Course written by Dragu Atanasiu and published by World Scientific. This book was released on 2020-03-26 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Linear Algebra and Matrices

Author : Helene Shapiro
Publisher : American Mathematical Soc.
ISBN 13 : 1470418525
Total Pages : 338 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Linear Algebra and Matrices by : Helene Shapiro

Download or read book Linear Algebra and Matrices written by Helene Shapiro and published by American Mathematical Soc.. This book was released on 2015-10-08 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A First Course in Linear Algebra

Author : Kenneth Kuttler
Publisher :
ISBN 13 :
Total Pages : 586 pages
Book Rating : 4.:/5 (125 download)

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Book Synopsis A First Course in Linear Algebra by : Kenneth Kuttler

Download or read book A First Course in Linear Algebra written by Kenneth Kuttler and published by . This book was released on 2020 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A First Course in Linear Algebra, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course for the general students who have an understanding of basic high school algebra and intend to be users of linear algebra methods in their profession, from business & economics to science students. All major topics of linear algebra are available in detail, as well as justifications of important results. In addition, connections to topics covered in advanced courses are introduced. The textbook is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the textbook."--BCcampus website.

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.

A First Course in Linear Algebra

Author : A. G. Hamilton
Publisher : CUP Archive
ISBN 13 : 9780521310413
Total Pages : 164 pages
Book Rating : 4.3/5 (14 download)

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Book Synopsis A First Course in Linear Algebra by : A. G. Hamilton

Download or read book A First Course in Linear Algebra written by A. G. Hamilton and published by CUP Archive. This book was released on 1987-09-03 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a short, readable introduction to basic linear algebra, as usually encountered in a first course. The development of the subject is integrated with a large number of worked examples that illustrate the ideas and methods. The format of the book, with text and relevant examples on facing pages means that the reader can follow the text uninterrupted. The student should be able to work through the book and learn from it sequentially. Stress is placed on applications of the methods rather than on developing a logical system of theorems. Numerous exercises are provided.

A First Course in Linear Algebra

Author : Minking Eie
Publisher : World Scientific Publishing Company
ISBN 13 : 9789813143111
Total Pages : 0 pages
Book Rating : 4.1/5 (431 download)

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Book Synopsis A First Course in Linear Algebra by : Minking Eie

Download or read book A First Course in Linear Algebra written by Minking Eie and published by World Scientific Publishing Company. This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The text itself is well-written. Each chapter begins with a brief synopsis which nicely captures the heart of the chapter, and there are enough boldface headings and vocabulary to keep the reader oriented to the task at hand." MAA Reviews A First Course in Linear Algebra is written by two experts from algebra who have more than 20 years of experience in algebra, linear algebra and number theory. It prepares students with no background in Linear Algebra. Students, after mastering the materials in this textbook, can already understand any Linear Algebra used in more advanced books and research papers in Mathematics or in other scientific disciplines. This book provides a solid foundation for the theory dealing with finite dimensional vector spaces. It explains in details the relation between linear transformations and matrices. One may thus use different viewpoints to manipulate a matrix instead of a one-sided approach. Although most of the examples are for real and complex matrices, a vector space over a general field is briefly discussed. Several optional sections are devoted to applications to demonstrate the power of Linear Algebra.

A First Course In Linear Algebra

Author : Shou-te Chang
Publisher : World Scientific Publishing Company
ISBN 13 : 9813143134
Total Pages : 389 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis A First Course In Linear Algebra by : Shou-te Chang

Download or read book A First Course In Linear Algebra written by Shou-te Chang and published by World Scientific Publishing Company. This book was released on 2016-07-13 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Course in Linear Algebra is written by two experts from algebra who have more than 20 years of experience in algebra, linear algebra and number theory. It prepares students with no background in Linear Algebra. Students, after mastering the materials in this textbook, can already understand any Linear Algebra used in more advanced books and research papers in Mathematics or in other scientific disciplines.This book provides a solid foundation for the theory dealing with finite dimensional vector spaces. It explains in details the relation between linear transformations and matrices. One may thus use different viewpoints to manipulate a matrix instead of a one-sided approach. Although most of the examples are for real and complex matrices, a vector space over a general field is briefly discussed. Several optional sections are devoted to applications to demonstrate the power of Linear Algebra.

A First Course in Linear Algebra

Author : Robert A. Beezer
Publisher : Congruent Press
ISBN 13 : 9780984417551
Total Pages : 542 pages
Book Rating : 4.4/5 (175 download)

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Book Synopsis A First Course in Linear Algebra by : Robert A. Beezer

Download or read book A First Course in Linear Algebra written by Robert A. Beezer and published by Congruent Press. This book was released on 2012-12-01 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the basic concepts of linear algebra, along with an introduction to the techniques of formal mathematics. Numerous worked examples and exercises, along with precise statements of definitions and complete proofs of every theorem, make the text ideal for independent study.

A First Course in Linear Algebra

Author : Daniel Zelinsky
Publisher : Academic Press
ISBN 13 : 1483265005
Total Pages : 277 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis A First Course in Linear Algebra by : Daniel Zelinsky

Download or read book A First Course in Linear Algebra written by Daniel Zelinsky and published by Academic Press. This book was released on 2014-05-12 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Course in Linear Algebra provides an introduction to the algebra and geometry of vectors, matrices, and linear transformations. This book is designed as a background for second-year courses in calculus of several variables and differential equations where the theory of linear differential equations parallels that of linear algebraic equations. The topics discussed include the multiplication of vectors by scalars, vectors in n-space, planes and lines, and composites of linear mappings. The symmetric matrices and mappings, quadratic forms, change of coordinates, and effect of change of basis on matrices of linear functions are also described. This text likewise considers the computation of determinants, diagonalizable transformations, computation of eigenvalues and eigenvectors, and principal axis theorem. This publication is suitable for college students taking a course in linear algebra.

Linear Algebra

Author : Larry E. Knop
Publisher : CRC Press
ISBN 13 : 1584887834
Total Pages : 748 pages
Book Rating : 4.5/5 (848 download)

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Book Synopsis Linear Algebra by : Larry E. Knop

Download or read book Linear Algebra written by Larry E. Knop and published by CRC Press. This book was released on 2008-08-28 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Algebra: A First Course with Applications explores the fundamental ideas of linear algebra, including vector spaces, subspaces, basis, span, linear independence, linear transformation, eigenvalues, and eigenvectors, as well as a variety of applications, from inventories to graphics to Google's PageRank. Unlike other texts on the subject, thi

Introduction to Linear and Matrix Algebra

Author : Nathaniel Johnston
Publisher : Springer Nature
ISBN 13 : 3030528111
Total Pages : 482 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Introduction to Linear and Matrix Algebra by : Nathaniel Johnston

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.

Linear Algebra: Core Topics For The Second Course

Author : Dragu Atanasiu
Publisher : World Scientific
ISBN 13 : 9811258562
Total Pages : 333 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Linear Algebra: Core Topics For The Second Course by : Dragu Atanasiu

Download or read book Linear Algebra: Core Topics For The Second Course written by Dragu Atanasiu and published by World Scientific. This book was released on 2023-01-04 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

First Course in Linear Algebra

Author : Phani Bhushan Bhattacharya
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 318 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis First Course in Linear Algebra by : Phani Bhushan Bhattacharya

Download or read book First Course in Linear Algebra written by Phani Bhushan Bhattacharya and published by John Wiley & Sons. This book was released on 1983 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advanced Linear Algebra

Author : Bruce Cooperstein
Publisher : CRC Press
ISBN 13 : 1439829691
Total Pages : 361 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Advanced Linear Algebra by : Bruce Cooperstein

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.

A First Course in Linear Algebra

Author : Raymond A. Beauregard
Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis A First Course in Linear Algebra by : Raymond A. Beauregard

Download or read book A First Course in Linear Algebra written by Raymond A. Beauregard and published by . This book was released on 1973 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applied Linear Algebra

Author : Peter J. Olver
Publisher : Springer
ISBN 13 : 3319910418
Total Pages : 702 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Applied Linear Algebra by : Peter J. Olver

Download or read book Applied Linear Algebra written by Peter J. Olver and published by Springer. This book was released on 2018-05-30 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the underlying linear algebraic techniques, thereby enabling students not only to learn how to apply the mathematical tools in routine contexts, but also to understand what is required to adapt to unusual or emerging problems. No previous knowledge of linear algebra is needed to approach this text, with single-variable calculus as the only formal prerequisite. However, the reader will need to draw upon some mathematical maturity to engage in the increasing abstraction inherent to the subject. Once equipped with the main tools and concepts from this book, students will be prepared for further study in differential equations, numerical analysis, data science and statistics, and a broad range of applications. The first author’s text, Introduction to Partial Differential Equations, is an ideal companion volume, forming a natural extension of the linear mathematical methods developed here.

Linear Algebra: Core Topics for the Second Course

Author : DRAGU. MIKUSINSKI ATANASIU (PIOTR.)
Publisher : World Scientific Publishing Company
ISBN 13 : 9789811258541
Total Pages : 0 pages
Book Rating : 4.2/5 (585 download)

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Book Synopsis Linear Algebra: Core Topics for the Second Course by : DRAGU. MIKUSINSKI ATANASIU (PIOTR.)

Download or read book Linear Algebra: Core Topics for the Second Course written by DRAGU. MIKUSINSKI ATANASIU (PIOTR.) and published by World Scientific Publishing Company. This book was released on 2022-11-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book for a 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. This is highly effective to create the needed depth of understanding a general theory by detailing a proof of a particular case that encapsulates the main idea of a general theorem. Using the knowledge gained from a particular case, it 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.