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 Introduction to Linear and Matrix Algebra written by Nathaniel Johnston and published by . This book was released on 2021 with total page 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 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 Matrices and Linear Algebra written by Hans Schneider and published by Courier Corporation. This book was released on 2012-06-08 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it. This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related topics such as determinants, eigenvalues, and differential equations. Table of Contents: l. The Algebra of Matrices 2. Linear Equations 3. Vector Spaces 4. Determinants 5. Linear Transformations 6. Eigenvalues and Eigenvectors 7. Inner Product Spaces 8. Applications to Differential Equations For the second edition, the authors added several exercises in each chapter and a brand new section in Chapter 7. The exercises, which are both true-false and multiple-choice, will enable the student to test his grasp of the definitions and theorems in the chapter. The new section in Chapter 7 illustrates the geometric content of Sylvester's Theorem by means of conic sections and quadric surfaces. 6 line drawings. lndex. Two prefaces. Answer section.
Download or read book Advanced Linear and Matrix Algebra written by Nathaniel Johnston and published by Springer Nature. This book was released on 2021-05-19 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Concise Introduction to Linear Algebra written by Qingwen Hu and published by CRC Press. This book was released on 2017-09-22 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise Introduction to Linear Algebra deals with the subject of linear algebra, covering vectors and linear systems, vector spaces, orthogonality, determinants, eigenvalues and eigenvectors, singular value decomposition. It adopts an efficient approach to lead students from vectors, matrices quickly into more advanced topics including, LU decomposition, orthogonal decomposition, Least squares solutions, Gram-Schmidt process, eigenvalues and eigenvectors, diagonalizability, spectral decomposition, positive definite matrix, quadratic forms, singular value decompositions and principal component analysis. This book is designed for onesemester teaching to undergraduate students.
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 A Unified Introduction to Linear Algebra written by Alan Tucker and published by MacMillan Publishing Company. This book was released on 1988 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Algebra written by Jim Hefferon and published by Orthogonal Publishing L3c. This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Download or read book Introduction to Linear Algebra written by Marvin Marcus and published by Courier Dover Publications. This book was released on 1988 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rigorous, self-contained introduction at undergraduate level covers vector spaces and linear transformations, linear equations and determinants, characteristic roots. Includes 16 sets of true-false quizzes and exercises — with worked-out solutions — a complete theory of permutations and much more.
Download or read book Introduction to Matrix Algebra written by Autar Kaw and published by Lulu.com. This book was released on 2008-09 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 2002, the Introduction to Matrix Algebra book has been downloaded by more than 30,000 users from 50 different countries. This book is an extended primer for undergraduate Matrix Algebra. The book is either to be used as a refresher material for students who have already taken a course in Matrix Algebra or used as a just-in-time tool if the burden of teaching Matrix Algebra has been placed on several courses. In my own department, the Linear Algebra course was taken out of the curriculum a decade ago. It is now taught just in time in courses like Statics, Programming Concepts, Vibrations, and Controls. There are ten chapters in the book 1) INTRODUCTION, 2) VECTORS, 3) BINARY MATRIX OPERATIONS, 4) UNARY MATRIX OPERATIONS, 5) SYSTEM OF EQUATIONS, 6) GAUSSIAN ELIMINATION, 7) LU DECOMPOSITION, 8) GAUSS-SEIDAL METHOD, 9) ADEQUACY OF SOLUTIONS, 10) EIGENVALUES AND EIGENVECTORS.
Download or read book Introduction to Linear Algebra written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Linear Algebra written by Gordon Mills and published by Routledge. This book was released on 2017-07-12 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction To Linear Algebra written by Mark J. DeBonis and published by CRC Press. This book was released on 2022-02-23 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Linear Algebra: Computation, Application, and Theory is designed for students who have never been exposed to the topics in a linear algebra course. The text is filled with interesting and diverse application sections but is also a theoretical text which aims to train students to do succinct computation in a knowledgeable way. After completing the course with this text, the student will not only know the best and shortest way to do linear algebraic computations but will also know why such computations are both effective and successful. Features: Includes cutting edge applications in machine learning and data analytics Suitable as a primary text for undergraduates studying linear algebra Requires very little in the way of pre-requisites
Download or read book Matrix Algebra for Linear Models written by Marvin H. J. Gruber and published by John Wiley & Sons. This book was released on 2013-12-31 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to matrix analysis theory and applications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models offers a succinct summary of matrix theory and its related applications to statistics, especially linear models. The book provides a unified presentation of the mathematical properties and statistical applications of matrices in order to define and manipulate data. Written for theoretical and applied statisticians, the book utilizes multiple numerical examples to illustrate key ideas, methods, and techniques crucial to understanding matrix algebra’s application in linear models. Matrix Algebra for Linear Models expertly balances concepts and methods allowing for a side-by-side presentation of matrix theory and its linear model applications. Including concise summaries on each topic, the book also features: Methods of deriving results from the properties of eigenvalues and the singular value decomposition Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhance understanding of the presented material Matrix Algebra for Linear Models is an ideal textbook for advanced undergraduate and graduate-level courses on statistics, matrices, and linear algebra. The book is also an excellent reference for statisticians, engineers, economists, and readers interested in the linear statistical model.
Download or read book Introduction to Linear Algebra and Differential Equations written by John W. Dettman and published by Courier Corporation. This book was released on 2012-10-05 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more. Includes 48 black-and-white illustrations. Exercises with solutions. Index.
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.
