Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on the proofs. Strang's emphasis is on providing understanding.
linear algebra and its applications
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Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text. Finally, when discussed in the abstract, these concepts are more accessible. Students conceptual understanding is reinforced through True/False questions, practice problems, and the use of technology. David Lay changed the study of linear algebra with the execution of this philosophy, and continues his quest to improve the way linear algebra is taught with the new Updated Second Edition. With this update he takes the instruction of linear algebra to a new level through inc
The Study Guide is based on David Lay's many years in the classroom, and has been updated so students can take full advantage of the new projects and data in the Updated Second Edition of the text. This guide gives the worked-out solutions to model problems that correspond with exercises in the text, along with study tips, hints to students, instructions for using MATLAB along with the text, additional MATLAB exercises, and expanded coverage of some text material. Maple and Mathematica appendices have been added, and the TI appendix has been updated to include coverage of the TI-86.
Linear Algebra and Its Applications, Second Edition fulfills the need for a book that will permit the teaching of the applications of linear algebra, in combination with the underlying mathematics. Comprised of eight chapters, the book aims to provide a comprehensive presentation of the concepts and methods in linear algebra. The text starts with the discussion of the Gaussian elimination, the simplest and most useful method of solution. This chapter is followed by chapters that focus on the study of vector spaces, projections and inner products, determinants, and eigenvalues. Discussions on positive definite matrices, computations with matrices, and introduction to linear programming and game theory are provided as well. This text is intended for use by college students.
Praise for the First Edition ". . .recommended for the teacher and researcher as well as forgraduate students. In fact, [it] has a place on everymathematician's bookshelf." -American Mathematical Monthly Linear Algebra and Its Applications, Second Edition presents linearalgebra as the theory and practice of linear spaces and linear mapswith a unique focus on the analytical aspects as well as thenumerous applications of the subject. In addition to thoroughcoverage of linear equations, matrices, vector spaces, game theory,and numerical analysis, the Second Edition featuresstudent-friendly additions that enhance the book's accessibility,including expanded topical coverage in the early chapters,additional exercises, and solutions to selected problems. Beginning chapters are devoted to the abstract structure of finitedimensional vector spaces, and subsequent chapters addressconvexity and the duality theorem as well as describe the basics ofnormed linear spaces and linear maps between normed spaces. Further updates and revisions have been included to reflect themost up-to-date coverage of the topic, including: The QR algorithm for finding the eigenvalues of a self-adjointmatrix The Householder algorithm for turning self-adjoint matricesinto tridiagonal form The compactness of the unit ball as a criterion of finitedimensionality of a normed linear space Additionally, eight new appendices have been added and cover topicssuch as: the Fast Fourier Transform; the spectral radius theorem;the Lorentz group; the compactness criterion for finitedimensionality; the characterization of commentators; proof ofLiapunov's stability criterion; the construction of the JordanCanonical form of matrices; and Carl Pearcy's elegant proof ofHalmos' conjecture about the numerical range of matrices. Clear, concise, and superbly organized, Linear Algebra and ItsApplications, Second Edition serves as an excellent text foradvanced undergraduate- and graduate-level courses in linearalgebra. Its comprehensive treatment of the subject also makes itan ideal reference or self-study for industry professionals.
From Tzuong-Tsieng Moh, a long-time expert in algebra, comes a new book for students to better understand linear algebra. Writing from an experienced standpoint, Moh touches on the many facets surrounding linear algebra, including but not limited to, echelon forms, matrix algebra, linear transformations, determinants, dual space, inner products, the Gram-Schmidt Theorem, Hilbert space, and more. It is ideal for both newcomers and seasoned readers who want to attain a deeper understanding on both the basics and advanced topics of linear algebra and its vast applications. The wide range of topics combined with the depth of each discussion make it essential to be on the shelf of every mathematical beginner and enthusiast.
This book deals with system of linear equations and their solutions by means of elementary row operations on matrices, vector spaces, subspaces, bases and dimensions, linear transformations, their algebra, their representations by matrices as well as isomorphism, linear functional and dual spaces, inner products, among others.
For courses in linear algebra. With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations) are not easily understood and require time to assimilate. These concepts are fundamental to the study of linear algebra, so students' understanding of them is vital to mastering the subject. This text makes these concepts more accessible by introducing them early in a familiar, concrete Rn setting, developing them gradually, and returning to them throughout the text so that when they are discussed in the abstract, students are readily able to understand. MyMathLab is an online homework, tutorial, and assessment product designed to personalize learning and improve results. With a wide range of interactive, engaging, and assignable activities, students are encouraged to actively learn and retain tough course concepts. Please note that the product you are purchasing does not include MyMathLab. MyMathLab Join over 11 million students benefiting from Pearson MyLabs. This title can be supported by MyMathLab, an online homework and tutorial system designed to test and build your understanding. Would you like to use the power of MyMathLab to accelerate your learning? You need both an access card and a course ID to access MyMathLab. These are the steps you need to take: 1. Make sure that your lecturer is already using the system Ask your lecturer before purchasing a MyLab product as you will need a course ID from them before you can gain access to the system. 2. Check whether an access card has been included with the book at a reduced cost If it has, it will be on the inside back cover of the book. 3. If you have a course ID but no access code, you can benefit from MyMathLab at a reduced price by purchasing a pack containing a copy of the book and an access code for MyMathLab (ISBN:9781292092348) 4. If your lecturer is using the MyLab and you would like to purchase the product... Go to www.mymathlab.com to buy access to this interactive study programme. For educator access, contact your Pearson representative. To find out who your Pearson representative is, visit www.pearsoned.co.uk/replocator