Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added.The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions.No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.From the reviews of previous editions:Altogether, the text is a didactic masterpiece. ― zbMATHThe determinant-free proofs are elegant and intuitive. ― American Mathematical MonthlyThe most original linear algebra book to appear in years, it certainly belongs in every undergraduate library ― CHOICE Read more

Linear algebra now rivals or surpasses calculus in importance for people working in quantitative fields of all kinds: engineers, scientists, economists and business people. Gilbert Strang has taught linear algebra at MIT for more than 50 years and the course he developed has become a model for teaching around the world. His video lectures on MIT OpenCourseWare have been viewed over ten million times and his twelve textbooks are popular with readers worldwide. This sixth edition of Professor Strang's most popular book, Introduction to Linear Algebra, introduces the ideas of independent columns and the rank and column space of a matrix early on for a more active start. Then the book moves directly to the classical topics of linear equations, fundamental subspaces, least squares, eigenvalues and singular values – in each case expressing the key idea as a matrix factorization. The final chapters of this edition treat optimization and learning from data: the most active application of linear algebra today. Everything is explained thoroughly in Professor Strang's characteristic clear style. It is sure to delight and inspire the delight and inspire the next generation of learners. Read more

Richard Silverman's translation enhances the accessibility and usability of Shilov's Linear Algebra text for English readers, ensuring clarity and comprehension. Georgi E. Shilov, Professor of Mathematics at the Moscow State University, covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers. Because it contains an abundance of problems and examples, the book will be useful for self-study as well as for the classroom.   Accessible and User-Friendly: Comprehensive Coverage: The book covers essential topics, including determinants, linear spaces, systems of linear equations, and coordinate transformations, providing a solid foundation for advanced studies. Clear Advanced Material: Starts with elementary content and seamlessly transitions into advanced areas, suitable for undergraduate and graduate courses. Abundant Practice Problems: Includes a plethora of problems with a dedicated section for hints and answers, facilitating self-study and reinforcing learning. Integrated Approach: Combines algebra, geometry, and analysis for a cohesive understanding of linear algebra concepts. Real-World Applications: Explores bilinear and quadratic forms, Euclidean and unitary spaces, and finite-dimensional algebras, providing practical and theoretical insights. Educationally Rich: Perfect for self-learners and classroom settings, offering extensive examples and exercises to enhance problem-solving skills. Appendix and Additional Resources: The appendix on categories of finite-dimensional spaces broadens the reader’s perspective and comprehension of the subject matter. Read more

Master the math needed to excel in data science, machine learning, and statistics. In this book author Thomas Nield guides you through areas like calculus, probability, linear algebra, and statistics and how they apply to techniques like linear regression, logistic regression, and neural networks. Along the way you'll also gain practical insights into the state of data science and how to use those insights to maximize your career. Learn how to: Use Python code and libraries like SymPy, NumPy, and scikit-learn to explore essential mathematical concepts like calculus, linear algebra, statistics, and machine learning Understand techniques like linear regression, logistic regression, and neural networks in plain English, with minimal mathematical notation and jargon Perform descriptive statistics and hypothesis testing on a dataset to interpret p-values and statistical significance Manipulate vectors and matrices and perform matrix decomposition Integrate and build upon incremental knowledge of calculus, probability, statistics, and linear algebra, and apply it to regression models including neural networks Navigate practically through a data science career and avoid common pitfalls, assumptions, and biases while tuning your skill set to stand out in the job market Read more

Linear algebra is the foundation of science and engineering. Knowledge of linear algebra is a prerequisite for studying statistics, machine learning, computer graphics, signal processing, chemistry, economics, quantum mechanics, and countless other applications. Indeed, linear algebra offers a powerful toolbox for modelling the real world.The NO BULLSHIT GUIDE TO LINEAR ALGEBRA shows the connections between the computational techniques of linear algebra, their geometric interpretations, and the theoretical foundations. This university-level textbook contains lessons on linear algebra written in a style that is precise and concise. Each concept is illustrated through definitions, formulas, diagrams, explanations, and examples of real-world applications. Readers build their math superpowers by solving practice problems and learning to use the computer algebra system SymPy to speed up tedious matrix arithmetic tasks.“The book explains the concepts in a way that gives a strong intuitive understanding.” — Joe Nestor, student“It’s very well written and a fun read!” — Felix Kwok, professor“I used this book in multiple big data courses when I needed a deeper understanding of the material.” — Zane Zakraisek, studentThe author, Ivan Savov, combines 15 years of tutoring experience with a B.Eng. in electrical engineering, an M.Sc. in physics, and a Ph.D. in computer science from McGill University. Read more

An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant xkcd comics. Chapters: The Function, The Field, The Vector, The Vector Space, The Matrix, The Basis, Dimension, Gaussian Elimination, The Inner Product, Special Bases, The Singular Value Decomposition, The Eigenvector, The Linear Program Read more

A complete quick reference guide for all aspects of Linear Algebra. Read more

Has the abstract nature of linear algebra ever left you overwhelmed? Do you yearn to unlock the essence of machine learning but are bogged down by the intricacy of the mathematics? Dive into a realm where linear algebra unfolds not just as numerical operations, but as a powerful story. A story intertwined with the magic of machine learning, making sense of data, and unraveling algorithms that power tomorrow.I am Jorge, a mathematician with over a decade of hands-on experience in data science and machine learning. Having navigated the intricate pathways of mathematical computations and machine learning algorithms myself, I wrote this book that differs itself from a traditional text book. With a conversational style and humour, I will guide through what you've been seeking on your journey into the depths of linear algebra.This book isn’t just about understanding linear algebra—it’s about experiencing it. Dive into real-world applications, and grasp concepts that are foundational to machine learning:Intuitive Understanding: Approach linear algebra as a story, where vectors and matrices come alive, making complex ideas feel intuitive and relatable.Comprehensive Coverage: From the basics of vector addition and matrix multiplication to advanced topics like eigen decomposition and principal component analysis, get a 360-degree understanding.Practical Applications: Discover how linear algebra powers algorithms, aiding in data interpretation and model building.Key takeaways include:Mastering vectors and matrices in real-world scenarios.The magic behind eigenvectors, eigenvalues, and their applications.Gaining insights into advanced topics like the singular value decomposition.And this is just the tip of the iceberg. Dive in to uncover the essence of machine learning through the lens of linear algebra, and let mathematics weave its story.Ready to embark on this transformative journey? Don't miss out—let the power of linear algebra unveil the mysteries of machine learning.24/01/2024 - UPDATESRefined definition of vectors spaces.New example of the dot product.Notation fixes.Complementary exercises. Grab your copy now! Read more

Learn to:Solve linear algebra equations in several waysPut data in order with matricesDetermine values with determinantsWork with eigenvalues and eigenvectorsYour hands-on guide to real-world applications of linear algebraDoes 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 matricesRelate vectors and linear transformations — link vectors and matrices with linear combinations and seek solutions of homogeneous systemsEvaluate determinants — see how to perform the determinant function on different sizes of matrices and take advantage of Cramer's ruleHone your skills with vector spaces — determine the properties of vector spaces and their subspaces and see linear transformation in actionTackle eigenvalues and eigenvectors — define and solve for eigenvalues and eigenvectors and understand how they interact with specific matricesOpen the book and find:Theoretical and practical ways of solving linear algebra problemsDefinitions of terms throughout and in the glossaryNew ways of looking at operationsHow linear algebra ties together vectors, matrices, determinants, and linear transformationsTen common mathematical representations of Greek lettersReal-world applications of matrices and determinants Read more

A Quick Steep Climb Up Lienar Algebra - and its companion site "allthemath" - are completely-and-forever-free-and-open-source educational materials dedicated to the mathematics that budding computer science practitioners actually need to know. They feature the fun and addictive teaching of award-winning lecturer Dr. Stephen Davies of the University of Mary Washington in Fredericksburg, Virginia! Read more

If you want to work in any computational or technical field, you need to understand linear algebra. As the study of matrices and operations acting upon them, linear algebra is the mathematical basis of nearly all algorithms and analyses implemented in computers. But the way it's presented in decades-old textbooks is much different from how professionals use linear algebra today to solve real-world modern applications. This practical guide from Mike X Cohen teaches the core concepts of linear algebra as implemented in Python, including how they're used in data science, machine learning, deep learning, computational simulations, and biomedical data processing applications. Armed with knowledge from this book, you'll be able to understand, implement, and adapt myriad modern analysis methods and algorithms. Ideal for practitioners and students using computer technology and algorithms, this book introduces you to: The interpretations and applications of vectors and matrices Matrix arithmetic (various multiplications and transformations) Independence, rank, and inverses Important decompositions used in applied linear algebra (including LU and QR) Eigendecomposition and singular value decomposition Applications including least-squares model fitting and principal components analysis Read more

Master the math needed to excel in data science, machine learning, and statistics. In this book author Thomas Nield guides you through areas like calculus, probability, linear algebra, and statistics and how they apply to techniques like linear regression, logistic regression, and neural networks. Along the way you'll also gain practical insights into the state of data science and how to use those insights to maximize your career.Learn how to:Use Python code and libraries like SymPy, NumPy, and scikit-learn to explore essential mathematical concepts like calculus, linear algebra, statistics, and machine learningUnderstand techniques like linear regression, logistic regression, and neural networks in plain English, with minimal mathematical notation and jargonPerform descriptive statistics and hypothesis testing on a dataset to interpret p-values and statistical significanceManipulate vectors and matrices and perform matrix decompositionIntegrate and build upon incremental knowledge of calculus, probability, statistics, and linear algebra, and apply it to regression models including neural networksNavigate practically through a data science career and avoid common pitfalls, assumptions, and biases while tuning your skill set to stand out in the job market Read more

For sophomore-level courses in Differential Equations and Linear Algebra. Extensively rewritten throughout, the Second Edition of this flexible text features a seamless integration of linear algebra into the discipline of differential equations. Abundant computer graphics, IDE interactive illustration software, and well-thought-out problem sets make it an excellent choice for either the combination DE/LA course or pure differential equations courses. The authors’ consistent, reader-friendly presentation encourages students to think both quantitatively and qualitatively when approaching differential equations — and reinforces concepts using similar methods to solve various systems (algebraic, differential, and iterative). Read more

Softcover exactly as pictured in very good, unmarked condition; NOT an old library book; In stock for fast shipping; Satisfaction is always guaranteed! Read more

Most introductory linear algebra textbooks follow one of two paths into the subject: abstract and arcane (beginning with the vector space axioms), or computational and colorless (beginning with systems of linear equations).The Dark Art of Linear Algebra takes a little-known third path that winds through a fascinating geometric landscape. Guided along it, readers encounter linear algebra's central objects - linear maps and the matrices that represent them - before they descend into the valley of linear systems. By emphasizing geometry over algorithms and intuition building over axiomatics, The Dark Art helps beginners grasp linear algebra’s great power and rare beauty. And it does this concisely: Students can read this book from cover to cover in a single course.All the usual introductory topics are here, presented with unusual clarity and style by Seth Braver, winner of the Mathematical Association of America's Beckenbach Book Prize for his first book, Lobachevski Illuminated. Read 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 matrices, large matrix computation techniques, compressed sensing, probability and statistics, optimization, the architecture of neural nets, stochastic gradient descent and backpropagation. Read more

Tough Test Questions? Missed Lectures? Not Enough Time? Textbook too Pricey?Fortunately, there's Schaum's. This all-in-one-package includes more than 600 fully-solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 25 detailed videos featuring math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible.More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. Helpful tables and illustrations increase your understanding of the subject at hand.Schaum’s Outline of Linear Algebra, Sixth Edition features: • Updated content to match the latest curriculum• Over 600 problems with step-by-step solutions• An accessible outline format for quick and easy review• Clear explanations for all linear algebra concepts• Access to revised Schaums.com website with access to 25 problem-solving videos, and more Read more

Are you ready to dive into the vibrant world of linear algebra and see how it powers real-world applications? Welcome to this comprehensive guide, where traditional theory meets modern computational practices.Linear algebra is the magic behind many computational sciences - machine learning, AI, data science, statistics, simulations, computer graphics, multivariate analyses, matrix decompositions, signal processing, and more. But here's a secret: the way it's taught in traditional textbooks isn't how professionals use it in the field.For instance, have you ever wondered about the practical importance of a matrix's "determinant"? You might be in for a surprise! This book bridges the gap between theoretical understanding and practical application, showing you not only the 'what' but also the 'how' of implementing linear algebra in real-world scenarios.What makes this book a must-have resource?Crystal clear explanations of linear algebra concepts and theories.Multiple angles to explain ideas, a proven technique to help cement your understanding.Vivid graphical visualizations to enhance your geometric intuition of linear algebra.Real-world implementations in MATLAB and Python. After all, in today's world, you seldom solve math problems by hand. Software is the way forward!A range of topics from beginner to intermediate levels, including vectors, matrix multiplications, least-squares projections, eigendecomposition, and singular-value decomposition.Emphasis on the application-oriented aspects of linear algebra and matrix analysis.Intuitive visual explanations of diagonalization, eigenvalues and eigenvectors, and singular value decomposition.Ready-to-use codes in MATLAB and Python to bring linear algebra concepts to life on your computer. All codes can be downloaded from https://github.com/mikexcohen/LinAlgBook.A unique blend of hand-solved exercises and advanced code challenges. Remember, math is not a spectator sport!Whether you're just starting your journey in linear algebra or seeking to apply these concepts to data analyses on computers (such as statistics or signal processing), this book is your go-to guide. With this book at your side, you won't just learn linear algebra; you'll experience it! Read more

Has the abstract nature of linear algebra ever left you overwhelmed? Do you yearn to unlock the essence of machine learning but are bogged down by the intricacy of the mathematics? Dive into a realm where linear algebra unfolds not just as numerical operations, but as a powerful story. A story intertwined with the magic of machine learning, making sense of data, and unraveling algorithms that power tomorrow.I am Jorge, a mathematician with over a decade of hands-on experience in data science and machine learning. Having navigated the intricate pathways of mathematical computations and machine learning algorithms myself, I wrote this book that differs itself from a traditional text book. With a conversational style and humour, I will guide through what you've been seeking on your journey into the depths of linear algebra.This book isn’t just about understanding linear algebra—it’s about experiencing it. Dive into real-world applications, and grasp concepts that are foundational to machine learning:Intuitive Understanding: Approach linear algebra as a story, where vectors and matrices come alive, making complex ideas feel intuitive and relatable.Comprehensive Coverage: From the basics of vector addition and matrix multiplication to advanced topics like eigen decomposition and principal component analysis, get a 360-degree understanding.Practical Applications: Discover how linear algebra powers algorithms, aiding in data interpretation and model building.Key takeaways include:Mastering vectors and matrices in real-world scenarios.The magic behind eigenvectors, eigenvalues, and their applications.Gaining insights into advanced topics like the singular value decomposition.And this is just the tip of the iceberg. Dive in to uncover the essence of machine learning through the lens of linear algebra, and let mathematics weave its story.Ready to embark on this transformative journey? Don't miss out—let the power of linear algebra unveil the mysteries of machine learning.24/01/2024 - UPDATESRefined definition of vectors spaces.New example of the dot product.Notation fixes.Complementary exercises.Grab your copy now! Read more

Unlock the Secrets Behind Mathematics' Most Essential Method!Whether you're a student tackling your first course, a scientist applying mathematical tools, or even a curious mind wondering how Google ranks webpages, this comprehensive textbook gently guides you from the fundamentals of solving simple equations through the most insightful matrix transformations and vector analysis. Dive deep into the most vital concepts underpinning modern mathematics, physics, engineering, data science, and more, simplifying even the most complex ideas clearly and intuitively.✅ Step-by-Step Clarity: Master key topics like Systems of Linear Equations, Gaussian Elimination, Matrix Operations, and Determinants with detailed walkthroughs that keep you confident every step of the way.✅ Conceptual Insights: Clearly understand abstract concepts such as Vector Spaces, Eigenvalues and Eigenvectors, Orthogonality, and Diagonalization through practical, engaging explanations and relatable examples.✅ Practical Mastery: Harness powerful techniques such as Singular Value Decomposition (SVD), LU and QR Factorizations, and the Least Squares Method to handle real-world problems in fields as diverse as economics, physics, machine learning, and computer graphics.Throughout these pages, numerous illustrative examples help ground your learning in real-world scenarios:Predicting population dynamics and ecological outcomes using matrix modeling.Using Google’s Page Rank algorithm explained through eigenvectors.Analyzing economic models and business forecasting with determinants and matrix algebra.Perfecting data-fitting and minimizing error in scientific experiments using Least Squares Approximations.Simplifying computations and visualizing data using Orthogonal Projections and the Gram-Schmidt Process.Structured precisely for learners at all levels, this book delivers clarity and versatility for self-study, classwork, and professional reference alike. Transform confusion into confidence, complexity into clarity, and linear algebra into your greatest mathematical asset.Take control of your understanding, boost your career prospects, and sharpen your analytical thinking today! Read more