Introduction To Linear And Matrix Algebra

Author : Nathaniel Johnston
Publisher : Springer Nature
Page : 482 pages
File Size : 43,6 Mb
Release : 2021-05-19
Category : Mathematics
ISBN : 9783030528119

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Introduction to Linear and Matrix Algebra by Nathaniel Johnston Pdf

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 : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 477 pages
File Size : 46,7 Mb
Release : 2018-06-07
Category : Business & Economics
ISBN : 9781316518960

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Introduction to Applied Linear Algebra by Stephen Boyd,Lieven Vandenberghe Pdf

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Author : Hans Schneider,George Phillip Barker
Publisher : Courier Corporation
Page : 432 pages
File Size : 53,6 Mb
Release : 2012-06-08
Category : Mathematics
ISBN : 9780486139302

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Matrices and Linear Algebra by Hans Schneider,George Phillip Barker Pdf

Basic textbook covers theory of matrices and its applications to systems of linear equations and related topics such as determinants, eigenvalues, and differential equations. Includes numerous exercises.

Author : L. Mirsky
Publisher : Courier Corporation
Page : 466 pages
File Size : 43,8 Mb
Release : 2012-12-03
Category : Mathematics
ISBN : 9780486166445

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An Introduction to Linear Algebra by L. Mirsky Pdf

Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter.

Author : Nathaniel Johnston
Publisher : Springer Nature
Page : 494 pages
File Size : 41,7 Mb
Release : 2021-05-19
Category : Mathematics
ISBN : 9783030528157

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Advanced Linear and Matrix Algebra by Nathaniel Johnston Pdf

This textbook emphasizes the interplay between algebra and geometry to motivate the study of advanced linear algebra techniques. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. Building on a first course in linear algebra, this book offers readers a deeper understanding of abstract structures, matrix decompositions, multilinearity, and tensors. Concepts draw on concrete examples throughout, offering accessible pathways to advanced techniques. Beginning with a study of vector spaces that includes coordinates, isomorphisms, orthogonality, and projections, the book goes on to focus on matrix decompositions. Numerous decompositions are explored, including the Shur, spectral, singular value, and Jordan decompositions. In each case, the author ties the new technique back to familiar ones, to create a coherent set of tools. Tensors and multilinearity complete the book, with a study of the Kronecker product, multilinear transformations, and tensor products. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from the QR and Cholesky decompositions, to matrix-valued linear maps and semidefinite programming. Exercises of all levels accompany each section. Advanced Linear and Matrix Algebra offers students of mathematics, data analysis, and beyond the essential tools and concepts needed for further study. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. A first course in proof-based linear algebra is assumed. An ideal preparation can be found in the author’s companion volume, Introduction to Linear and Matrix Algebra.

Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 290 pages
File Size : 41,8 Mb
Release : 2012-10-17
Category : Mathematics
ISBN : 9780486623184

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Linear Algebra and Matrix Theory by Robert R. Stoll Pdf

Advanced undergraduate and first-year graduate students have long regarded this text as one of the best available works on matrix theory in the context of modern algebra. Teachers and students will find it particularly suited to bridging the gap between ordinary undergraduate mathematics and completely abstract mathematics. The first five chapters treat topics important to economics, psychology, statistics, physics, and mathematics. Subjects include equivalence relations for matrixes, postulational approaches to determinants, and bilinear, quadratic, and Hermitian forms in their natural settings. The final chapters apply chiefly to students of engineering, physics, and advanced mathematics. They explore groups and rings, canonical forms for matrixes with respect to similarity via representations of linear transformations, and unitary and Euclidean vector spaces. Numerous examples appear throughout the text.

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210702

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Introduction to Linear Algebra by Serge Lang Pdf

This 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 : Steven Roman
Publisher : Springer Science & Business Media
Page : 486 pages
File Size : 44,5 Mb
Release : 2007-12-31
Category : Mathematics
ISBN : 9780387274744

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Advanced Linear Algebra by Steven Roman Pdf

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 : Géza Schay
Publisher : Springer Science & Business Media
Page : 338 pages
File Size : 49,8 Mb
Release : 2012-03-30
Category : Mathematics
ISBN : 9780817683252

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A Concise Introduction to Linear Algebra by Géza Schay Pdf

Building on the author's previous edition on the subject (Introduction to Linear Algebra, Jones & Bartlett, 1996), this book offers a refreshingly concise text suitable for a standard course in linear algebra, presenting a carefully selected array of essential topics that can be thoroughly covered in a single semester. Although the exposition generally falls in line with the material recommended by the Linear Algebra Curriculum Study Group, it notably deviates in providing an early emphasis on the geometric foundations of linear algebra. This gives students a more intuitive understanding of the subject and enables an easier grasp of more abstract concepts covered later in the course. The focus throughout is rooted in the mathematical fundamentals, but the text also investigates a number of interesting applications, including a section on computer graphics, a chapter on numerical methods, and many exercises and examples using MATLAB. Meanwhile, many visuals and problems (a complete solutions manual is available to instructors) are included to enhance and reinforce understanding throughout the book. Brief yet precise and rigorous, this work is an ideal choice for a one-semester course in linear algebra targeted primarily at math or physics majors. It is a valuable tool for any professor who teaches the subject.

Author : Gordon Mills
Publisher : Routledge
Page : 181 pages
File Size : 44,9 Mb
Release : 2017-07-12
Category : Mathematics
ISBN : 9781351511568

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Introduction to Linear Algebra by Gordon Mills Pdf

This is the first book on linear algebra written specifically for social scientists. It deals only with those aspects of the subject applicable in the social sciences and provides a thorough understanding of linear algebra for those who wish to use it as a tool in the design, execution, and interpretation of research. Linear mathematical models play an important role in all of the social sciences. This book provides a step-by-step introduction to those parts of linear algebra which are useful in such model building. It illustrates some of the applications of linear analysis and helps the reader learn how to convert his formulation of a social science problem into algebraic terms. The author covers matrix algebra, computational methods, linear models involving discrete variables, and clear, complete explanations of necessary mathematical concepts. Prior knowledge of calculus is not required since no use is made of calculus or of complex numbers. A novel feature of the mathematical content of the book is the treatment of models expressed in terms of variables which must be whole numbers (integers). The book is distinguished by a step-by-step exposition that allows the reader to grasp quickly and fully the principles of linear algebra. All of the examples used to illustrate the text are drawn from the social sciences, enabling the reader to relate the subject to concrete problems in his field. Exercises are included as a necessary part of the text to develop points not covered in the text and to provide practice in the algebraic formulation of applied problems. An appendix gives solutions (or hints) for selected exercises.

Author : Alan Tucker
Publisher : MacMillan Publishing Company
Page : 570 pages
File Size : 55,6 Mb
Release : 1988
Category : Algebras, Linear
ISBN : UCSC:32106019498804

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A Unified Introduction to Linear Algebra by Alan Tucker Pdf

Author : Daniel Norman,Dan Wolczuk
Publisher : Unknown
Page : 528 pages
File Size : 51,9 Mb
Release : 2011-12-15
Category : Algebras, Linear
ISBN : 0321748964

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An Introduction to Linear Algebra for Science and Engineering by Daniel Norman,Dan Wolczuk Pdf

Norman/Wolczuk's An Introduction to Linear Algebra for Science and Engineering has been widely respected for its unique approach, which helps students understand and apply theory and concepts by combining theory with computations and slowly bringing students to the difficult abstract concepts. This approach includes an early treatment of vector spaces and complex topics in a simpler, geometric context. An Introduction to Linear Algebra for Science and Engineering promotes advanced thinking and understanding by encouraging students to make connections between previously learned and new concepts and demonstrates the importance of each topic through applications. NEW! MyMathLab is now available for this text. The course features assignable homework exercises plus the complete eBook, in addition to tutorial and assessment tools that make it easy to manage your course online.

Author : Jim Hefferon
Publisher : Orthogonal Publishing L3c
Page : 128 pages
File Size : 41,5 Mb
Release : 2015
Category : Algebras, Linear
ISBN : 0989897567

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Linear Algebra by Jim Hefferon Pdf

"This text covers a standard first course : Gauss's method, vector spaces, linear maps and matrices, determinants, and eigenvalues and eigenvectors. In addition, each chapter ends with some topics such as brief applications. What sets it apart is careful motivation, many examples, and extensive exercise sets. Together these help each student master the material of this course, and also help an instructor develop that student's level of mathematical maturity. This book has been available online for many years and is widely used, both in classrooms and for self-study. It is supported by worked answers for all exercises, beamer slides for classroom use, and a lab manual of computer work"--Page 4 of cover.

Author : Tai-Ran Hsu
Publisher : John Wiley & Sons
Page : 536 pages
File Size : 50,8 Mb
Release : 2018-04-30
Category : Technology & Engineering
ISBN : 9781119071204

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Applied Engineering Analysis by Tai-Ran Hsu Pdf

A resource book applying mathematics to solve engineering problems Applied Engineering Analysis is a concise textbookwhich demonstrates how toapply mathematics to solve engineering problems. It begins with an overview of engineering analysis and an introduction to mathematical modeling, followed by vector calculus, matrices and linear algebra, and applications of first and second order differential equations. Fourier series and Laplace transform are also covered, along with partial differential equations, numerical solutions to nonlinear and differential equations and an introduction to finite element analysis. The book also covers statistics with applications to design and statistical process controls. Drawing on the author's extensive industry and teaching experience, spanning 40 years, the book takes a pedagogical approach and includes examples, case studies and end of chapter problems. It is also accompanied by a website hosting a solutions manual and PowerPoint slides for instructors. Key features: Strong emphasis on deriving equations, not just solving given equations, for the solution of engineering problems. Examples and problems of a practical nature with illustrations to enhance student’s self-learning. Numerical methods and techniques, including finite element analysis. Includes coverage of statistical methods for probabilistic design analysis of structures and statistical process control (SPC). Applied Engineering Analysis is a resource book for engineering students and professionals to learn how to apply the mathematics experience and skills that they have already acquired to their engineering profession for innovation, problem solving, and decision making.

Author : Gordon Mills
Publisher : Routledge
Page : 237 pages
File Size : 46,8 Mb
Release : 2017-07-12
Category : Mathematics
ISBN : 9781351511575

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Introduction to Linear Algebra by Gordon Mills Pdf

This is the first book on linear algebra written specifically for social scientists. It deals only with those aspects of the subject applicable in the social sciences and provides a thorough understanding of linear algebra for those who wish to use it as a tool in the design, execution, and interpretation of research. Linear mathematical models play an important role in all of the social sciences. This book provides a step-by-step introduction to those parts of linear algebra which are useful in such model building. It illustrates some of the applications of linear analysis and helps the reader learn how to convert his formulation of a social science problem into algebraic terms. The author covers matrix algebra, computational methods, linear models involving discrete variables, and clear, complete explanations of necessary mathematical concepts. Prior knowledge of calculus is not required since no use is made of calculus or of complex numbers. A novel feature of the mathematical content of the book is the treatment of models expressed in terms of variables which must be whole numbers (integers). The book is distinguished by a step-by-step exposition that allows the reader to grasp quickly and fully the principles of linear algebra. All of the examples used to illustrate the text are drawn from the social sciences, enabling the reader to relate the subject to concrete problems in his field. Exercises are included as a necessary part of the text to develop points not covered in the text and to provide practice in the algebraic formulation of applied problems. An appendix gives solutions (or hints) for selected exercises.