*Xian Xing Dai Shu (Di 5 Ban)*

**Author**: Gilbert Strang

**Publisher:**

**ISBN:**

**Category:** Algebras, Linear

**Page:** 573

**View:** 236

Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains all the qualities of earlier editions while at the same time seeing numerous minor improvements and major additions. The latter include: • A new chapter on singular values and singular vectors, including ways to analyze a matrix of data • A revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages • A new section on linear algebra and cryptography • A new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (e.g. practice problems, exams, development of textbook examples), plus codes in MATLAB, Julia, and Python.

Originally published in 2002, reissued as part of Pearson's modern classic series.

Mathematics

Linear algebra is a pillar of machine learning. You cannot develop a deep understanding and application of machine learning without it. In this laser-focused Ebook, you will finally cut through the equations, Greek letters, and confusion, and discover the topics in linear algebra that you need to know. Using clear explanations, standard Python libraries, and step-by-step tutorial lessons, you will discover what linear algebra is, the importance of linear algebra to machine learning, vector, and matrix operations, matrix factorization, principal component analysis, and much more.

Linear algebra and the foundations of deep learning, together at last! From Professor Gilbert Strang, acclaimed author of Introduction to Linear Algebra, comes Linear Algebra and Learning from Data, the first textbook that teaches linear algebra together with deep learning and neural nets. This readable yet rigorous textbook contains a complete course in the linear algebra and related mathematics that students need to know to get to grips with learning from data. Included are: the four fundamental subspaces, singular value decompositions, special marices, large matrix computation techniques, compressed sensing, probability and statistics, optimization, the architecture of neural nets, stochastic gradient descent and backpropagation.

Elementary Linear Algebra, 5th edition, by Stephen Andrilli and David Hecker, is a textbook for a beginning course in linear algebra for sophomore or junior mathematics majors. This text provides a solid introduction to both the computational and theoretical aspects of linear algebra. The textbook covers many important real-world applications of linear algebra, including graph theory, circuit theory, Markov chains, elementary coding theory, least-squares polynomials and least-squares solutions for inconsistent systems, differential equations, computer graphics and quadratic forms. Also, many computational techniques in linear algebra are presented, including iterative methods for solving linear systems, LDU Decomposition, the Power Method for finding eigenvalues, QR Decomposition, and Singular Value Decomposition and its usefulness in digital imaging. The most unique feature of the text is that students are nurtured in the art of creating mathematical proofs using linear algebra as the underlying context. The text contains a large number of worked out examples, as well as more than 970 exercises (with over 2600 total questions) to give students practice in both the computational aspects of the course and in developing their proof-writing abilities. Every section of the text ends with a series of true/false questions carefully designed to test the students’ understanding of the material. In addition, each of the first seven chapters concludes with a thorough set of review exercises and additional true/false questions. Supplements to the text include an Instructor’s Manual with answers to all of the exercises in the text, and a Student Solutions Manual with detailed answers to the starred exercises in the text. Finally, there are seven additional web sections available on the book’s website to instructors who adopt the text. Builds a foundation for math majors in reading and writing elementary mathematical proofs as part of their intellectual/professional development to assist in later math courses Presents each chapter as a self-contained and thoroughly explained modular unit. Provides clearly written and concisely explained ancillary materials, including four appendices expanding on the core concepts of elementary linear algebra Prepares students for future math courses by focusing on the conceptual and practical basics of proofs

This print textbook is available for students to rent for their classes. The Pearson print rental program provides students with affordable access to learning materials, so they come to class ready to succeed. For courses in Linear Algebra. Fosters the concepts and skills students will use in future careers Linear Algebra and Its Applications offers a modern elementary introduction with broad, relevant applications. With traditional texts, the early stages of the course are relatively easy as material is presented in a familiar, concrete setting; but students often hit a wall when abstract concepts are introduced. Certain concepts fundamental to the study of linear algebra (such as linear independence, vector space, and linear transformations) require time to learn-and students' understanding of them is vital. Lay, Lay, and McDonald make 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 students can grasp them when they are discussed in the abstract. Throughout, the 6th Edition updates exercises, adds new applications, takes advantage of improved technology, and offers more support for conceptual learning. Also available with MyLab Math By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student. 0135851254 / 9780135851258 LINEAR ALGEBRA AND ITS APPLICATIONS [RENTAL EDITION], 6/e

Designed for undergraduate and postgraduate students of mathematics, the book can also be used by those preparing for various competitive examinations. The text starts with a brief introduction to results from Set theory and Number theory. It then goes on to cover Groups, Rings, Fields and Linear Algebra. The topics under groups include subgroups, finitely generated abelian groups, group actions, solvable and nilpotent groups. The course in ring theory covers ideals, embedding of rings, Euclidean domains, PIDs, UFDs, polynomial rings, Noetherian (Artinian) rings. Topics of field include algebraic extensions, splitting fields, normal extensions, separable extensions, algebraically closed fields, Galois extensions, and construction by ruler and compass. The portion on linear algebra deals with vector spaces, linear transformations, Eigen spaces, diagonalizable operators, inner product spaces, dual spaces, operators on inner product spaces etc. The theory has been strongly supported by numerous examples and worked-out problems. There is also plenty of scope for the readers to try and solve problems on their own.New in this Edition• A full section on operators in inner product spaces.• Complete survey of finite groups of order up to 15 and Wedderburn theorem on finite division rings.• Addition of around one hundred new worked-out problems and examples.• Alternate and simpler proofs of some results.• A new section on quick recall of various useful results at the end of the book to facilitate the reader to get instant answers to tricky questions.