Linear Algebra Essentials

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Essential Linear Algebra with Applications

Author : Titu Andreescu
Publisher : Springer
ISBN 13 : 0817646361
Total Pages : 498 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Essential Linear Algebra with Applications by : Titu Andreescu

Download or read book Essential Linear Algebra with Applications written by Titu Andreescu and published by Springer. This book was released on 2014-10-14 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rooted in a pedagogically successful problem-solving approach to linear algebra, the present work fills a gap in the literature that is sharply divided between elementary texts and books that are too advanced to appeal to a wide audience. It clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while simultaneously emphasizing applications and connections to fields such as biology, economics, computer graphics, electrical engineering, cryptography, and political science. Ideal as an introduction to linear algebra, the extensive exercises and well-chosen applications also make this text suitable for advanced courses at the junior or senior undergraduate level. Furthermore, it can serve as a colorful supplementary problem book, reference, or self-study manual for professional scientists and mathematicians. Complete with bibliography and index, "Essential Linear Algebra with Applications" is a natural bridge between pure and applied mathematics and the natural and social sciences, appropriate for any student or researcher who needs a strong footing in the theory, problem-solving, and model-building that are the subject’s hallmark.

Fundamentals of Linear Algebra

Author : J.S. Chahal
Publisher : CRC Press
ISBN 13 : 0429758103
Total Pages : 184 pages
Book Rating : 4.4/5 (297 download)

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Book Synopsis Fundamentals of Linear Algebra by : J.S. Chahal

Download or read book Fundamentals of Linear Algebra written by J.S. Chahal and published by CRC Press. This book was released on 2018-12-07 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Linear Algebra is like no other book on the subject. By following a natural and unified approach to the subject it has, in less than 250 pages, achieved a more complete coverage of the subject than books with more than twice as many pages. For example, the textbooks in use in the United States prove the existence of a basis only for finite dimensional vector spaces. This book proves it for any given vector space. With his experience in algebraic geometry and commutative algebra, the author defines the dimension of a vector space as its Krull dimension. By doing so, most of the facts about bases when the dimension is finite, are trivial consequences of this definition. To name one, the replacement theorem is no longer needed. It becomes obvious that any two bases of a finite dimensional vector space contain the same number of vectors. Moreover, this definition of the dimension works equally well when the geometric objects are nonlinear. Features: Presents theories and applications in an attempt to raise expectations and outcomes The subject of linear algebra is presented over arbitrary fields Includes many non-trivial examples which address real-world problems About the Author: Dr. J.S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published a number of papers about number theory. For hobbies, he likes to travel and hike, the reason he accepted the position at Brigham Young University

No Bullshit Guide to Linear Algebra

Author : Ivan Savov
Publisher :
ISBN 13 : 9780992001025
Total Pages : 596 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis No Bullshit Guide to Linear Algebra by : Ivan Savov

Download or read book No Bullshit Guide to Linear Algebra written by Ivan Savov and published by . This book was released on 2020-10-25 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook covers the material for an undergraduate linear algebra course: vectors, matrices, linear transformations, computational techniques, geometric constructions, and theoretical foundations. The explanations are given in an informal conversational tone. The book also contains 100+ problems and exercises with answers and solutions. A special feature of this textbook is the prerequisites chapter that covers topics from high school math, which are necessary for learning linear algebra. The presence of this chapter makes the book suitable for beginners and the general audience-readers need not be math experts to read this book. Another unique aspect of the book are the applications chapters (Ch 7, 8, and 9) that discuss applications of linear algebra to engineering, computer science, economics, chemistry, machine learning, and even quantum mechanics.

Basics of Matrix Algebra for Statistics with R

Author : Nick Fieller
Publisher : CRC Press
ISBN 13 : 1315360055
Total Pages : 208 pages
Book Rating : 4.3/5 (153 download)

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Book Synopsis Basics of Matrix Algebra for Statistics with R by : Nick Fieller

Download or read book Basics of Matrix Algebra for Statistics with R written by Nick Fieller and published by CRC Press. This book was released on 2018-09-03 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Thorough Guide to Elementary Matrix Algebra and Implementation in R Basics of Matrix Algebra for Statistics with R provides a guide to elementary matrix algebra sufficient for undertaking specialized courses, such as multivariate data analysis and linear models. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject. The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. The text explores how these concepts arise in statistical techniques, including principal component analysis, canonical correlation analysis, and linear modeling. In addition to the algebraic manipulation of matrices, the book presents numerical examples that illustrate how to perform calculations by hand and using R. Many theoretical and numerical exercises of varying levels of difficulty aid readers in assessing their knowledge of the material. Outline solutions at the back of the book enable readers to verify the techniques required and obtain numerical answers. Avoiding vector spaces and other advanced mathematics, this book shows how to manipulate matrices and perform numerical calculations in R. It prepares readers for higher-level and specialized studies in statistics.

Linear Algebra

Author : Przemyslaw Bogacki
Publisher : American Mathematical Soc.
ISBN 13 : 1470443848
Total Pages : 397 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Linear Algebra by : Przemyslaw Bogacki

Download or read book Linear Algebra written by Przemyslaw Bogacki and published by American Mathematical Soc.. This book was released on 2019-01-24 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Algebra: Concepts and Applications is designed to be used in a first linear algebra course taken by mathematics and science majors. It provides a complete coverage of core linear algebra topics, including vectors and matrices, systems of linear equations, general vector spaces, linear transformations, eigenvalues, and eigenvectors. All results are carefully, clearly, and rigorously proven. The exposition is very accessible. The applications of linear algebra are extensive and substantial—several of those recur throughout the text in different contexts, including many that elucidate concepts from multivariable calculus. Unusual features of the text include a pervasive emphasis on the geometric interpretation and viewpoint as well as a very complete treatment of the singular value decomposition. The book includes over 800 exercises and numerous references to the author's custom software Linear Algebra Toolkit.

Handbook of Linear Algebra, Second Edition

Author : Leslie Hogben
Publisher : CRC Press
ISBN 13 : 1466507284
Total Pages : 1906 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Handbook of Linear Algebra, Second Edition by : Leslie Hogben

Download or read book Handbook of Linear Algebra, Second Edition written by Leslie Hogben and published by CRC Press. This book was released on 2013-11-26 with total page 1906 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters. New to the Second Edition Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems More chapters on applications of linear algebra, including epidemiology and quantum error correction New chapter on using the free and open source software system Sage for linear algebra Additional sections in the chapters on sign pattern matrices and applications to geometry Conjectures and open problems in most chapters on advanced topics Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.

Basic Linear Algebra

Author : T.S. Blyth
Publisher : Springer Science & Business Media
ISBN 13 : 1447106814
Total Pages : 242 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Basic Linear Algebra by : T.S. Blyth

Download or read book Basic Linear Algebra written by T.S. Blyth and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers: this will take the form of a tutorial on the use of the "LinearAlgebra" package in MAPLE 7 and will deal with all the aspects of linear algebra developed within the book.

Introduction to Linear Algebra

Author : Frank M. Stewart
Publisher : Courier Dover Publications
ISBN 13 : 0486841510
Total Pages : 307 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Introduction to Linear Algebra by : Frank M. Stewart

Download or read book Introduction to Linear Algebra written by Frank M. Stewart and published by Courier Dover Publications. This book was released on 2019-07-17 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Linear Algebra stresses finite dimensional vector spaces and linear transformations. Intended for undergraduate majors in mathematics, applied mathematics, chemistry, and physics, the treatment's only prerequisite is a first course in calculus. Proofs are given in detail, and carefully chosen problems demonstrate the variety of situations in which these concepts arise. After a brief Introduction, the text advances to chapters on the plane, linear dependence, span, dimension, bases, and subspaces. Subsequent chapters explore linear transformations, the dual space in terms of multilinear forms and determinants, a traditional treatment of determinants, and inner product spaces. Extensive Appendixes cover equations and identities; variables, quantifiers, and unknowns; sets; proofs; indices and summations; and functions.

Linear Algebra For Dummies

Author : Mary Jane Sterling
Publisher : John Wiley & Sons
ISBN 13 : 0470538163
Total Pages : 387 pages
Book Rating : 4.4/5 (75 download)

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Book Synopsis Linear Algebra For Dummies by : Mary Jane Sterling

Download or read book Linear Algebra For Dummies written by Mary Jane Sterling and published by John Wiley & Sons. This book was released on 2009-06-05 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn to: Solve linear algebra equations in several ways Put data in order with matrices Determine values with determinants Work with eigenvalues and eigenvectors Your hands-on guide to real-world applications of linear algebra Does linear algebra leave you feeling lost? No worries this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction. Line up the basics discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices Relate vectors and linear transformations link vectors and matrices with linear combinations and seek solutions of homogeneous systems Evaluate determinants see how to perform the determinant function on different sizes of matrices and take advantage of Cramer's rule Hone your skills with vector spaces determine the properties of vector spaces and their subspaces and see linear transformation in action Tackle eigenvalues and eigenvectors define and solve for eigenvalues and eigenvectors and understand how they interact with specific matrices Open the book and find: Theoretical and practical ways of solving linear algebra problems Definitions of terms throughout and in the glossary New ways of looking at operations How linear algebra ties together vectors, matrices, determinants, and linear transformations Ten common mathematical representations of Greek letters Real-world applications of matrices and determinants

Introduction to Linear Algebra and Differential Equations

Author : John W. Dettman
Publisher : Courier Corporation
ISBN 13 : 0486158314
Total Pages : 442 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Introduction to Linear Algebra and Differential Equations by : John W. Dettman

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.

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.

How to Prove It

Author : Daniel J. Velleman
Publisher : Cambridge University Press
ISBN 13 : 0521861241
Total Pages : 401 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis How to Prove It by : Daniel J. Velleman

Download or read book How to Prove It written by Daniel J. Velleman and published by Cambridge University Press. This book was released on 2006-01-16 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

Introduction to Linear Algebra

Author : Marvin Marcus
Publisher : Courier Dover Publications
ISBN 13 : 9780486656953
Total Pages : 0 pages
Book Rating : 4.6/5 (569 download)

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Book Synopsis Introduction to Linear Algebra by : Marvin Marcus

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.

An Introduction to Wavelets Through Linear Algebra

Author : M.W. Frazier
Publisher : Springer
ISBN 13 : 3642855709
Total Pages : 517 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis An Introduction to Wavelets Through Linear Algebra by : M.W. Frazier

Download or read book An Introduction to Wavelets Through Linear Algebra written by M.W. Frazier and published by Springer. This book was released on 2013-12-11 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics majors at Michigan State University take a "Capstone" course near the end of their undergraduate careers. The content of this course varies with each offering. Its purpose is to bring together different topics from the undergraduate curriculum and introduce students to a developing area in mathematics. This text was originally written for a Capstone course. Basic wavelet theory is a natural topic for such a course. By name, wavelets date back only to the 1980s. On the boundary between mathematics and engineering, wavelet theory shows students that mathematics research is still thriving, with important applications in areas such as image compression and the numerical solution of differential equations. The author believes that the essentials of wavelet theory are sufficiently elementary to be taught successfully to advanced undergraduates. This text is intended for undergraduates, so only a basic background in linear algebra and analysis is assumed. We do not require familiarity with complex numbers and the roots of unity.

College Algebra

Author : Jay Abramson
Publisher :
ISBN 13 : 9789888407439
Total Pages : 892 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis College Algebra by : Jay Abramson

Download or read book College Algebra written by Jay Abramson and published by . This book was released on 2018-01-07 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt: College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory

Principles of Linear Algebra with Mathematica

Author : Kenneth M. Shiskowski
Publisher : John Wiley & Sons
ISBN 13 : 1118627261
Total Pages : 624 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Principles of Linear Algebra with Mathematica by : Kenneth M. Shiskowski

Download or read book Principles of Linear Algebra with Mathematica written by Kenneth M. Shiskowski and published by John Wiley & Sons. This book was released on 2013-06-07 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: A hands-on introduction to the theoretical and computational aspects of linear algebra using Mathematica® Many topics in linear algebra are simple, yet computationally intensive, and computer algebra systems such as Mathematica® are essential not only for learning to apply the concepts to computationally challenging problems, but also for visualizing many of the geometric aspects within this field of study. Principles of Linear Algebra with Mathematica uniquely bridges the gap between beginning linear algebra and computational linear algebra that is often encountered in applied settings, and the commands required to solve complex and computationally challenging problems using Mathematica are provided. The book begins with an introduction to the commands and programming guidelines for working with Mathematica. Next, the authors explore linear systems of equations and matrices, applications of linear systems and matrices, determinants, inverses, and Cramer's rule. Basic linear algebra topics, such as vectors, dot product, cross product, and vector projection are explored, as well as a unique variety of more advanced topics including rotations in space, 'rolling' a circle along a curve, and the TNB Frame. Subsequent chapters feature coverage of linear transformations from Rn to Rm, the geometry of linear and affine transformations, with an exploration of their effect on arclength, area, and volume, least squares fits, and pseudoinverses. Mathematica is used to enhance concepts and is seamlessly integrated throughout the book through symbolic manipulations, numerical computations, graphics in two and three dimensions, animations, and programming. Each section concludes with standard problems in addition to problems that were specifically designed to be solved with Mathematica, allowing readers to test their comprehension of the presented material. All related Mathematica code is available on a corresponding website, along with solutions to problems and additional topical resources. Extensively class-tested to ensure an accessible presentation, Principles of Linear Algebra with Mathematica is an excellent book for courses on linear algebra at the undergraduate level. The book is also an ideal reference for students and professionals who would like to gain a further understanding of the use of Mathematica to solve linear algebra problems.

Linear Algebra and Learning from Data

Author : Gilbert Strang
Publisher : Wellesley-Cambridge Press
ISBN 13 : 9780692196380
Total Pages : 0 pages
Book Rating : 4.1/5 (963 download)

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Book Synopsis Linear Algebra and Learning from Data by : Gilbert Strang

Download or read book Linear Algebra and Learning from Data written by Gilbert Strang and published by Wellesley-Cambridge Press. This book was released on 2019-01-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 matrices, large matrix computation techniques, compressed sensing, probability and statistics, optimization, the architecture of neural nets, stochastic gradient descent and backpropagation.