Linear Algebra For Everyone

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Linear Algebra for Everyone

Linear Algebra for Everyone
  • Author : Gilbert Strang
  • Publisher : Unknown
  • Release Date : 2020-11-26
  • Total pages : 368
  • ISBN : 1733146636
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Summary : Linear algebra has become the subject to know for people in quantitative disciplines of all kinds. No longer the exclusive domain of mathematicians and engineers, it is now used everywhere there is data and everybody who works with data needs to know more. This new book from Professor Gilbert Strang, author of the acclaimed Introduction to Linear Algebra, now in its fifth edition, makes linear algebra accessible to everybody, not just those with a strong background in mathematics. It takes a more active start, beginning by finding independent columns of small matrices, leading to the key concepts of linear combinations and rank and column space. From there it passes on to the classical topics of solving linear equations, orthogonality, linear transformations and subspaces, all clearly explained with many examples and exercises. The last major topics are eigenvalues and the important singular value decomposition, illustrated with applications to differential equations and image compression. A final optional chapter explores the ideas behind deep learning.

Linear Algebra for Everyone

Linear Algebra for Everyone
  • Author : Lorenzo Robbiano
  • Publisher : Unknown
  • Release Date : 2011-05-09
  • Total pages : 218
  • ISBN : 9788847018396
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Summary : This book provides students with the rudiments of Linear Algebra, a fundamental subject for students in all areas of science and technology. The book would also be good for statistics students studying linear algebra. It is the translation of a successful textbook currently being used in Italy. The author is a mathematician sensitive to the needs of a general audience. In addition to introducing fundamental ideas in Linear Algebra through a wide variety of interesting examples, the book also discusses topics not usually covered in an elementary text (e.g. the "cost" of operations, generalized inverses, approximate solutions). The challenge is to show why the "everyone" in the title can find Linear Algebra useful and easy to learn. The translation has been prepared by a native English speaking mathematician, Professor Anthony V. Geramita.

Linear Algebra and Learning from Data

Linear Algebra and Learning from Data
  • Author : Gilbert Strang
  • Publisher : Unknown
  • Release Date : 2019-01-31
  • Total pages : 446
  • ISBN : 0692196382
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Summary : 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.

Introduction to Applied Linear Algebra

Introduction to Applied Linear Algebra
  • Author : Stephen Boyd,Lieven Vandenberghe
  • Publisher : Unknown
  • Release Date : 2018-06-07
  • Total pages : 500
  • ISBN : 9781316518960
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Summary : A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Introduction to Linear Algebra

Introduction to Linear Algebra
  • Author : Gilbert Strang
  • Publisher : Unknown
  • Release Date : 2016-08-11
  • Total pages : 600
  • ISBN : 0980232775
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Summary : 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.

Introduction to Linear Algebra

Introduction to Linear Algebra
  • Author : Gilbert Strang
  • Publisher : Unknown
  • Release Date : 1993
  • Total pages : 472
  • ISBN : STANFORD:36105007523389
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Summary : Book Description: Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'. Introduction to Linear Algebra, Fourth Edition includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course is followed by seven applications: differential equations, engineering, graph theory, statistics, Fourier methods and the FFT, linear programming, and computer graphics. Thousands of teachers in colleges and universities and now high schools are using this book, which truly explains this crucial subject.

Linear Algebra

Linear Algebra
  • Author : Kuldeep Singh
  • Publisher : Unknown
  • Release Date : 2013-10
  • Total pages : 608
  • ISBN : 9780199654444
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Summary : "This book is intended for first- and second-year undergraduates arriving with average mathematics grades ... The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to all of the set problems freely available online http://www.oup.co.uk/companion/singh" -- From preface.

Linear Algebra Done Right

Linear Algebra Done Right
  • Author : Sheldon Axler
  • Publisher : Unknown
  • Release Date : 1997-07-18
  • Total pages : 251
  • ISBN : 0387982590
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Summary : 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.

Linear Algebra For Dummies

Linear Algebra For Dummies
  • Author : Mary Jane Sterling
  • Publisher : Unknown
  • Release Date : 2009-06-05
  • Total pages : 384
  • ISBN : 9780470538166
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Summary : 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

An Introduction to Linear Algebra

An Introduction to Linear Algebra
  • Author : L. Mirsky
  • Publisher : Unknown
  • Release Date : 2012-12-03
  • Total pages : 464
  • ISBN : 9780486166445
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Summary : 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.

Linear Algebra as an Introduction to Abstract Mathematics

Linear Algebra as an Introduction to Abstract Mathematics
  • Author : Isaiah Lankham,Bruno Nachtergaele,Anne Schilling
  • Publisher : Unknown
  • Release Date : 2015-11-30
  • Total pages : 208
  • ISBN : 9789814723794
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Summary : This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.

The Linear Algebra a Beginning Graduate Student Ought to Know

The Linear Algebra a Beginning Graduate Student Ought to Know
  • Author : Jonathan S. Golan
  • Publisher : Unknown
  • Release Date : 2012-04-23
  • Total pages : 497
  • ISBN : 9789400726369
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Summary : Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as to computer science, to the physical, biological, and social sciences, and to engineering. It encompasses an extensive corpus of theoretical results as well as a large and rapidly-growing body of computational techniques. Unfortunately, in the past decade, the content of linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or computational background. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the mathematics of the numerical algorithms they need for applications. Certainly, the material presented in the average undergraduate course is insufficient for graduate study. This book is intended to fill the gap which has developed by providing enough theoretical and computational material to allow the advanced undergraduate or beginning graduate student to overcome this deficiency and be able to work independently or in advanced courses. The book is intended to be used either as a self-study guide, a textbook for a course in advanced linear algebra, or as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some of the basic ideas and techniques, such as manipulation of small matrices and the solution of small systems of linear equations over the real numbers. More importantly, it assumes a seriousness of purpose, considerable motivation, and a modicum of mathematical sophistication on the part of the reader. In the latest edition, new major theorems have been added, as well as many new examples. There are over 130 additional exercises and many of the previous exercises have been revised or rewritten. In addition, a large number of additional biographical notes and thumbnail portraits of mathematicians have been included.

Mathematics for Machine Learning

Mathematics for Machine Learning
  • Author : Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong
  • Publisher : Unknown
  • Release Date : 2020-03-31
  • Total pages : 398
  • ISBN : 9781108470049
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Summary : Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.

Linear Algebra

Linear Algebra
  • Author : Hugo J. Woerdeman
  • Publisher : Unknown
  • Release Date : 2021-03-05
  • Total pages : 262
  • ISBN : 9781000345872
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Summary : This book is intended for a first linear algebra course. The text includes all essential topics in a concise manner and can therefore be fully covered in a one term course. After this course, the student is fully equipped to specialize further in their direction(s) of choice (advanced pure linear algebra, numerical linear algebra, optimization, multivariate statistics, or one of the many other areas of linear algebra applications). Linear Algebra is an exciting area of mathematics that is gaining more and more importance as the world is becoming increasingly digital. It has the following very appealing features: It is a solid axiomatic based mathematical theory that is accessible to a large variety of students. It has a multitude of applications from many different fields, ranging from traditional science and engineering applications to more ‘daily life’ applications (internet searches, guessing consumer preferences, etc.). It easily allows for numerical experimentation through the use of a variety of readily available software (both commercial and open source). This book incorporates all these aspects throughout the whole text with the intended effect that each student can find their own niche in the field. Several suggestions of different software are made. While MATLAB is certainly still a favorite choice, open source programs such as Sage (especially among algebraists) and the Python libraries are increasingly popular. This text guides the student through different programs by providing specific commands.

Quantum Computing for Everyone

Quantum Computing for Everyone
  • Author : Chris Bernhardt
  • Publisher : Unknown
  • Release Date : 2019-03-19
  • Total pages : 216
  • ISBN : 9780262350945
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Summary : An accessible introduction to an exciting new area in computation, explaining such topics as qubits, entanglement, and quantum teleportation for the general reader. Quantum computing is a beautiful fusion of quantum physics and computer science, incorporating some of the most stunning ideas from twentieth-century physics into an entirely new way of thinking about computation. In this book, Chris Bernhardt offers an introduction to quantum computing that is accessible to anyone who is comfortable with high school mathematics. He explains qubits, entanglement, quantum teleportation, quantum algorithms, and other quantum-related topics as clearly as possible for the general reader. Bernhardt, a mathematician himself, simplifies the mathematics as much as he can and provides elementary examples that illustrate both how the math works and what it means. Bernhardt introduces the basic unit of quantum computing, the qubit, and explains how the qubit can be measured; discusses entanglement—which, he says, is easier to describe mathematically than verbally—and what it means when two qubits are entangled (citing Einstein's characterization of what happens when the measurement of one entangled qubit affects the second as “spooky action at a distance”); and introduces quantum cryptography. He recaps standard topics in classical computing—bits, gates, and logic—and describes Edward Fredkin's ingenious billiard ball computer. He defines quantum gates, considers the speed of quantum algorithms, and describes the building of quantum computers. By the end of the book, readers understand that quantum computing and classical computing are not two distinct disciplines, and that quantum computing is the fundamental form of computing. The basic unit of computation is the qubit, not the bit.

A (terse) Introduction to Linear Algebra

A (terse) Introduction to Linear Algebra
  • Author : Yitzhak Katznelson,Yonatan R. Katznelson
  • Publisher : Unknown
  • Release Date : 2008
  • Total pages : 215
  • ISBN : 9780821844199
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Summary : Linear algebra is the study of vector spaces and the linear maps between them. It underlies much of modern mathematics and is widely used in applications. A (Terse) Introduction to Linear Algebra is a concise presentation of the core material of the subject--those elements of linear algebra that every mathematician, and everyone who uses mathematics, should know. It goes from the notion of a finite-dimensional vector space to the canonical forms of linear operators and their matrices, and covers along the way such key topics as: systems of linear equations, linear operators and matrices, determinants, duality, and the spectral theory of operators on inner-product spaces. The last chapter offers a selection of additional topics indicating directions in which the core material can be applied. The Appendix provides all the relevant background material. Written for students with some mathematical maturity and an interest in abstraction and formal reasoning, the book is self-contained and is appropriate for an advanced undergraduate course in linear algebra.

Applied Numerical Linear Algebra

Applied Numerical Linear Algebra
  • Author : James W. Demmel
  • Publisher : Unknown
  • Release Date : 1997-08-01
  • Total pages : 419
  • ISBN : 9780898713893
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Summary : This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.

Differential Equations and Linear Algebra

Differential Equations and Linear Algebra
  • Author : Gilbert Strang
  • Publisher : Unknown
  • Release Date : 2015-02-12
  • Total pages : 510
  • ISBN : 0980232791
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Summary : Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.

Linear Algebra

Linear Algebra
  • Author : Richard Bronson,Gabriel B. Costa
  • Publisher : Unknown
  • Release Date : 2007
  • Total pages : 503
  • ISBN : 9780120887842
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Summary : In this appealing and well-written text, Richard Bronson gives readers a substructure for a firm understanding of the abstract concepts of linear algebra and its applications. The author starts with the concrete and computational, and leads the reader to a choice of major applications (Markov chains, least-squares approximation, and solution of differential equations using Jordan normal form). The first three chapters address the basics: matrices, vector spaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructor's taste and to the length of the course. Bronson's approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced. Key material is highlighted in the text and summarized at the end of each chapter. The book also includes ample exercises with answers and hints. With its inclusion of all the needed features, this text will be a pleasure for professionals, teachers, and students. - Introduces deductive reasoning and helps the reader develop a facility with mathematical proofs - Gives computational algorithms for finding eigenvalues and eigenvectors - Provides a balanced approach to computation and theory - Superb motivation and writing - Excellent exercise sets, ranging from drill to theoretical/challeging - Useful and interesting applications not found in other introductory linear algebra texts

Lecture Notes for Linear Algebra

Lecture Notes for Linear Algebra
  • Author : Gilbert Strang
  • Publisher : Unknown
  • Release Date : 2022
  • Total pages : 186
  • ISBN : 9781733146647
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Summary : Lecture Notes for Linear Algebra provides instructors with a detailed lecture-by-lecture outline for a basic linear algebra course. The ideas and examples presented in this e-book are based on Strang’s video lectures for Mathematics 18.06 and 18.065, available on MIT’s OpenCourseWare (ocw.mit.edu) and YouTube (youtube.com/mitocw). Readers will quickly gain a picture of the whole course—the structure of the subject, the key topics in a natural order, and the connecting ideas that make linear algebra so beautiful.

Introduction to Linear Algebra

Introduction to Linear Algebra
  • Author : Gilbert Strang
  • Publisher : Unknown
  • Release Date : 2009-02-10
  • Total pages : 585
  • ISBN : 0980232716
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Summary : This leading textbook for first courses in linear algebra comes from the hugely experienced MIT lecturer and author Gilbert Strang. The book's tried and tested approach is direct, offering practical explanations and examples, while showing the beauty and variety of the subject. Unlike most other linear algebra textbooks, the approach is not a repetitive drill. Instead it inspires an understanding of real mathematics. The book moves gradually and naturally from numbers to vectors to the four fundamental subspaces. This new edition includes challenge problems at the end of each section. Preview five complete sections at math.mit.edu/linearalgebra. Readers can also view freely available online videos of Gilbert Strang's 18.06 linear algebra course at MIT, via OpenCourseWare (ocw.mit.edu), that have been watched by over a million viewers. Also on the web (http://web.mit.edu/18.06/www/), readers will find years of MIT exam questions, MATLAB help files and problem sets to practise what they have learned.