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

'Introduction to Linear Algebra' is specifically tailored for high school students, providing a clear and accessible understanding of the essential concepts while keeping their math level in mind. The book covers a wide range of topics, including matrices, determinants, vector spaces, linear transformations, and eigenvalues and eigenvectors.Through carefully crafted explanations, illustrative examples, and exercises, readers will develop a strong foundation in linear algebra and gain the skills necessary to apply these concepts to real-world problems. Read more

There are many reasons why neural networks fascinate us and have captivated headlines in recent years. They make web searches better, organize photos, and are even used in speech translation. Heck, they can even generate encryption. At the same time, they are also mysterious and mind-bending: how exactly do they accomplish these things ? What goes on inside a neural network? On a high level, a network learns just like we do, through trial and error. This is true regardless if the network is supervised, unsupervised, or semi-supervised. Once we dig a bit deeper though, we discover that a handful of mathematical functions play a major role in the trial and error process. It also becomes clear that a grasp of the underlying mathematics helps clarify how a network learns. In the following chapters we will unpack the mathematics that drive a neural network. To do this, we will use a feedforward network as our model and follow input as it moves through the network. Read more

Precalculus for Legends: Synthetic Division, Exponentials, Logarithms, Matrices, Partial Fractions, and SequencesAre you ready to take action and master essential precalculus topics? This book is inspired by the principles of Real Superpowers That Will Change Your Life and is part of the Superpowered Mathematics Series, designed to empower you to dive into math with confidence and energy.This fun and approachable guide focuses on key topics often encountered in algebra and precalculus courses, helping you build specific skills that will prepare you for calculus and beyond.What You’ll Find in This Book:Synthetic Division: A straightforward way to divide polynomials.Exponentials and Logarithms: Master exponentials and logarithms through practice.Matrices: Understand the power of arrays and how to manipulate them.Partial Fractions: Learn to decompose complex fractions into manageable parts.Sequences: Dive into patterns and progressions to sharpen your problem-solving skills.Why You’ll Love This Book:Action-Oriented: Inspired by Real Superpowers That Will Change Your Life, this book focuses on action, helping you get hands-on with math.Concise and Focused: A quick, enjoyable read with varied topics that keep things fresh and engaging.Complete Solutions: Full solutions to problems are included, so you can practice with confidence.If you’re ready to stop overthinking and start doing, this book is your gateway to mathematical success.Let’s GO! Take action now and become a math legend! Read more

Overcome Uncertainty with Logic and Reason.Life is full of uncertainties. You can't predict everything, but you can control the controllable by applying logic and reason. This book will introduce you to new ways of thinking and solving problems more efficiently. Discover how strategic games model real-life behavior and how many game theory concepts impact your daily life.Unlock the Power of Game Theory for Rational Decision-Making.Game theory, a branch of mathematics, focuses on rational, strategic decision-making. It applies to various fields, including psychology, economics, politics, military strategy, business, and retail pricing. By studying conflict and cooperation between intelligent, rational players, you’ll learn how to optimize decisions by considering others' actions. This book goes beyond theory, offering practical life skills to enhance your decision-making through strategic analysis.Boost Your Confidence in Decision-Making.Predict the future with greater accuracy. Wondering how to ask for a raise, choose the perfect date spot, or how top athletes and companies like Nike or Adidas make their best moves? Extraordinary decisions lead to outstanding success. By applying game theory principles, you’ll gain confidence in your choices.Learn Game Theory is written in a casual, easy-to-follow style with abundant relevant examples. It will help you develop strategic thinking, making better decisions based on logic and analysis.Transform Your Life with Game Theory.Make Better Business Decisions: Enhance your business strategies and optimize outcomes.Improve Your Relationships: Apply strategic thinking to build stronger, more effective relationships.Understand People Around You: Gain insights into human behavior and motivations.Navigate Sticky Situations: Develop skills to handle challenging scenarios more effectively.Albert Rutherford is an internationally bestselling author whose writing derives from various sources, such as research, coaching, academic, and real-life experience.Make better decisions and solve problems with ease. Learn Game Theory reveals the well-guarded secrets of great decision-makers. Read more

Comprehensive presentation of the theory, algebra, and properties of matrices and determinants. Read more

The essential reference book on matrices—now fully updated and expanded, with new material on scalar and vector mathematicsSince its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject.Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more.Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index.Fully updated and expanded with new material on scalar and vector mathematicsCovers the latest results in matrix theoryProvides a list of symbols and a summary of conventions for easy and precise useIncludes an extensive bibliography with back-referencing plus an author index Read more

Algebra II For Dummies, 2nd Edition (9781119543145) was previously published as Algebra II For Dummies, 2nd Edition (9781119090625). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.  Your complete guide to acing Algebra II Do quadratic equations make you queasy? Does the mere thought of logarithms make you feel lethargic? You're not alone! Algebra can induce anxiety in the best of us, especially for the masses that have never counted math as their forte. But here's the good news: you no longer have to suffer through statistics, sequences, and series alone. Algebra II For Dummies takes the fear out of this math course and gives you easy-to-follow, friendly guidance on everything you'll encounter in the classroom and arms you with the skills and confidence you need to score high at exam time.Gone are the days that Algebra II is a subject that only the serious 'math' students need to worry about. Now, as the concepts and material covered in a typical Algebra II course are consistently popping up on standardized tests like the SAT and ACT, the demand for advanced guidance on this subject has never been more urgent. Thankfully, this new edition of Algebra II For Dummies answers the call with a friendly and accessible approach to this often-intimidating subject, offering you a closer look at exponentials, graphing inequalities, and other topics in a way you can understand. Examine exponentials like a proFind out how to graph inequalitiesGo beyond your Algebra I knowledgeAce your Algebra II exams with easeWhether you're looking to increase your score on a standardized test or simply succeed in your Algebra II course, this friendly guide makes it possible.  Read more

Book Description:Unlock the full potential of matrix mathematics with this comprehensive guide that takes you from the basics to advanced topics in an easy-to-understand manner. Whether you're a student delving into linear algebra or a professional looking to refine your mathematical skills, this book covers it all. Each chapter provides detailed explanations, practical examples, and insightful tips to deepen your understanding of matrix operations and their applications in real-world scenarios.Key Features:Comprehensive Coverage: Offers a wide-ranging exploration of matrix mathematics from basic operations to complex theorems.Step-by-Step Explanations: Each topic is broken down into manageable steps with clear instructions and illustrative examples.Advanced Techniques: Covers cutting-edge methods and contemporary applications in various fields such as data science, statistical mechanics, and control theory.Practical Applications: Demonstrates how matrix theory applies to engineering, physics, computer science, and more.What You Will Learn:Master fundamental matrix operations such as addition, subtraction, and multiplication.Understand and apply scalar multiplication in various contexts.Discover the importance and calculation of matrix determinants.Delve into cofactor expansion for determinant computation.Learn methods to find the inverse of square matrices.Apply Gaussian elimination for solving linear equation systems.Utilize LU and Cholesky decompositions to simplify matrix equations.Familiarize yourself with QR decomposition and its applications.Explore eigenvalues and eigenvectors, including their computation and significance.Develop proficiency with characteristic polynomials and diagonalization.Employ singular value decomposition for data analysis.Compute and apply different matrix norms, including Frobenius and spectral norms.Calculate the trace and exponentiation of matrices, including fast techniques.Grasp the Hadamard and Kronecker products and their uses.Implement the Moore-Penrose inverse in linear algebra problems.Transform matrices to row echelon and reduced row echelon forms.Work with elementary matrices for row operations.Achieve matrices in Jordan normal form and understand its criteria.Determine matrix rank and apply the rank-nullity theorem.Use the Gerschgorin circle theorem for eigenvalue estimation.Assess the positive definiteness of matrices using Sylvester's criterion.Interpret the Binet-Cauchy theorem in matrix computations.Conceptualize matrix similarity and the Cayley-Hamilton theorem.Partition matrices effectively and employ block matrix multiplication.Deal with specialized matrices like Toeplitz, circulant, Hermitian, and skew-Hermitian matrices.Harness the power of orthogonal and projection matrices in preserving vector properties.Utilize Householder transformations and Givens rotations for numerical stability.Explore advanced topics such as matrix pencils, sparse matrices, and matrix completion.Attack complex matrix equations including Lyapunov, Sylvester, and algebraic Riccati equations.Leverage matrix functions and factorization in solving polynomials.Analyze tensors with matrix operations and delve into matrix calculus.Examine random matrices and apply the power method for eigenvalue approximation.Navigate through the QR algorithm, Lanczos algorithm, Arnoldi iteration, and Jacobi method for efficient eigenvalue computation.Conduct Schur decomposition to simplify complex matrix calculations. Read more

In this book, we introduce matrices and discuss their basic properties. The concepts of matrix addition, subtraction, and multiplication are introduced in a clear, step-by-step manner. Many examples are given throughout to aid in the understanding and execution of new concepts, sometimes making use of color to illustrate more complicated ideas. Square, diagonal, identity, and zero matrices are also discussed and explained at length with several examples. The goal of this book is to teach students a practical way of thinking about what matrices are and how they work, in a way suitable for all students. We strongly believe in teaching by examples, and that repetition is the best way to internalize new ideas. Each example intends to guide the student through the thinking process without skipping steps and touches on all of the new material presented.Now available in Spanish: Conceptos matemáticos - Introducción a las matrices (http://www.amazon.com/Conceptos-matem%C3%A1ticos-Introducci%C3%B3n-matrices-ebook/dp/B00811WWAG/ref=sr_1_1?ie=UTF8&qid=1337300188&sr=8-1) Read more

Become a Python Programming Expert With Ease! Python is a simple yet powerful programming language that can enable you to start thinking like a programmer right from the beginning. It is very readable and the stress many beginners face about memorizing arcane syntax typically presented by other programming languages will not affect you at all. Conversely, you will be able to concentrate on learning concepts and paradigms of programming. This book shall introduce you to an easy way to learn Python in just 7 days and in this time, be able to complete your own projects! By reading the book and implementing what you learn herein, you will realize just why major institutions like NASA, Google, Mozilla, Yahoo, Dropbox, IBM, Facebook and many others prefer to use python in their core products, services and business processes. Let’s begin. Here what you'll learn after downloading this Python for Beginners book: ✓Introduction ✓Chapter 1: Python: A Comprehensive Background ✓Chapter 2: How to Download and Install Python ✓Chapter 3: Python Glossary ✓Chapter 4: Interacting with Python ✓Chapter 5: Using Turtle for a Simple Drawing ✓Chapter 6: Variables ✓Chapter 7: Loops ✓Chapter 8: Native Python Datatypes ✓Chapter 9: Python Dictionaries ✓Chapter 10: Boolean Logic and Conditional Statements ✓Chapter 11: Constructing ‘While’ Loops In Python Chapter 12: Constructing ‘For Loops’ In Python Programming ✓Chapter 13: Constructing Classes and Defining Objects This Book Is Perfect For: ✓- Total beginners with zero programming experience ✓- Returning professionals who haven’t written code in years ✓- Seasoned professionals looking for a fast, simple, crash course in Python Download your copy today! Read more

Math Refresher for Adults: The Ultimate Step-by-Step Guide to Boost Your Math SkillsReclaim your confidence in math and make numbers work for you!Have you ever struggled with basic math tasks, hesitated to help your child with homework, or felt unprepared for exams? You’re not alone—and Math Refresher for Adults is here to help. This comprehensive guide is designed for anyone who wants to break free from math anxiety, learn at their own pace, and rediscover the power of numbers.Packed with clear explanations, relatable examples, and engaging exercises, this book will transform the way you approach math. Whether you’re refreshing your skills for career advancement, preparing for college entrance exams, or tackling everyday calculations, this is the resource you’ve been waiting for.What You’ll Learn Inside:Conquer Math Anxiety: Break down intimidating concepts into simple, manageable steps that anyone can understand.Build a Strong Foundation: Master numbers, operations, fractions, percentages, and other core topics with ease.Solve Real-World Problems: Budget your finances, calculate tips, interpret data, and confidently tackle everyday scenarios.Unlock Algebraic Power: Simplify expressions, solve equations, and graph solutions with clear, practical methods.Discover Geometry Essentials: Calculate areas, perimeters, and volumes, and navigate angles and shapes like a pro.Master Statistics and Probability: Learn to find averages, understand probabilities, and analyze data effectively.Ace Financial Math: Gain confidence in handling interest rates, loan calculations, and budgeting strategies.Identify Weak Spots: Use diagnostic quizzes and reflection questions to focus on areas that need the most attention.Get Extra Practice: Dive into a downloadable bonus workbook with additional exercises, solutions, and tools to reinforce your learning.and so, so much more...Unlike typical math textbooks, Math Refresher for Adults is designed to empower, inspire, and make learning enjoyable. You’ll feel supported every step of the way, thanks to:Clear Explanations: No jargon, no fluff—just straightforward guidance that makes sense.Practical Examples: Relatable scenarios that show how math connects to everyday life.Flexible Learning: Work through the chapters at your own pace or jump straight to the topics you need most.Inspirational Stories: Read testimonials from real people who’ve transformed their math skills—and their lives.This isn’t just a refresher—it’s a game-changer. By the time you finish this book, you’ll not only have a solid grasp of math concepts but also the confidence to apply them in your personal, academic, and professional life.Don’t wait—take the first step toward math mastery today. Order your copy now and make numbers your ally, not your enemy! Read more

Principal component analysis is probably the most extraordinary method of data analysis ever devised. With a simple linear operation we can tease out expression, age and sex from raw photographs. We can tell chimpanzee from human by the shape of a shoulder bone, and we can guess where someone lives, just from their DNA.The method is easy to explain and easy to apply. But that doesn’t tell you where the magic comes from. It doesn’t tell you why a linear operation should be enough to turn a frowning person into a smiling one.For that, we need to dig deeper. We need to dig up the foundations. That’s what this book is for. It starts with a quick and to-the-point introduction to what principal component analysis is, and how it works.Then, it peels back the layers of the onion one by one. We dive into eigenvectors and -values, the spectral theorem, the singular value decomposition and rank decompositions.Along the way, we’ll touch on subjects like complex numbers, determinants, characteristic polynomials and the fundamental theorem of algebra. We’ll do our best to cover them in the most intuitive way possible, with plenty of examples and illustrations. But the most important rule is that we leave no stone unturned. We will explain everything down to the foundations, without skipping any steps. Read more

Check out a complete series of videos on YouTube: http://bit.ly/YT4AMZHALA ! We answer all the questions left in the comments section. This book is for current linear algebra students looking to master the concepts of the subject, and for those who have taken it in the past looking for a refresher. It's an easy read which aims to illustrate concepts with examples and exercises. Linear algebra is a grand subject. Because it is fundamentally different from any high school mathematics, and because of the wildly varying quality of instructors, not all students enjoy learning it. In either case, whether you loved it or hated it, it takes several passes to learn linear algebra to the point that it becomes one of your favorite tools, one of your favorite ways of thinking about practical problems. This little textbook invites you on your second pass at linear algebra. Of course, your second pass may take place alongside your first pass. You may find this textbook particularly useful if you are studying for a test. Our goal is to take a step back from the mechanics of the subject with an eye towards gaining a larger view. A larger view, however, is achieved in small steps. We are not hoping for a big revelation but for a few small aha! moments. It simply takes time to put together the grand puzzle of linear algebra. You will get there, and the point, as the cliche goes, is to enjoy the ride. Psychology in mathematics is everything. I chose the topics according to the impact I feel they would make on your relationship with linear algebra. The textbook's utmost goal is to make you feel positively about the subject. You will find that some topics are surprisingly simple, others surprisingly tough. Some topics have important applications, others have none at all. Some were well presented in your linear algebra course, others skipped altogether. However, I hope you will find that all topics bring you a little closer to the subject of linear algebra. 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. Read more

Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related topics such as determinants, eigenvalues, and differential equations.Table of Contents:l. The Algebra of Matrices2. Linear Equations3. Vector Spaces4. Determinants5. Linear Transformations6. Eigenvalues and Eigenvectors7. Inner Product Spaces8. Applications to Differential EquationsFor the second edition, the authors added several exercises in each chapter and a brand new section in Chapter 7. The exercises, which are both true-false and multiple-choice, will enable the student to test his grasp of the definitions and theorems in the chapter. The new section in Chapter 7 illustrates the geometric content of Sylvester's Theorem by means of conic sections and quadric surfaces. 6 line drawings. lndex. Two prefaces. Answer section. Read more

This concise, plain-language guide for senior undergraduates and graduate students aims to develop intuition, practical skills and an understanding of the framework of numerical methods for the physical sciences and engineering. It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods. Topics are carefully selected and structured to build understanding, and illustrate key principles such as: accuracy, stability, order of convergence, iterative refinement, and computational effort estimation. Enrichment sections and in-depth footnotes form a springboard to more advanced material and provide additional background. Whether used for self-study, or as the basis of an accelerated introductory class, this compact textbook provides a thorough grounding in computational physics and engineering. Read more

This book is a short introuduction to various types of matrices. It contains a summary of elementary results on matrices with examples. This book would be useful for university students as well as lecturers. This book contains more than 300 examples of matrices. Read more

Boost your chances of scoring higher at Algebra IIAlgebra II introduces students to complex algebra concepts in preparation for trigonometry and calculus. In this new edition of Algebra II Workbook For Dummies, high school and college students will work through the types of Algebra II problems they'll see in class, including systems of equations, matrices, graphs, and conic sections. Plus, the book now comes with free 1-year access to chapter quizzes online! A recent report by ACT shows that over a quarter of ACT-tested 2012 high school graduates did not meet any of the four college readiness benchmarks in mathematics, English, reading, and science. Algebra II Workbook For Dummies presents tricky topics in plain English and short lessons, with examples and practice at every step to help students master the essentials, setting them up for success with each new lesson.Tracks to a typical Algebra II classCan be used as a supplement to classroom learning or for test prepIncludes plenty of practice and examples throughoutComes with free access to chapter quizzes onlineGet ready to take the intimidation out of Algebra II! Read more

Written as a guide to using matrices as a mathematical tool, this text is geared toward physical and social scientists, engineers, economists, and others who require a model for procedure rather than an exposition of theory. Knowledge of elementary algebra is the only mathematical prerequisite. Detailed numerical examples illustrate the treatment's focus on computational methods. The first four chapters outline the basic concepts of matrix theory. Topics include the development of the concept of elementary operations and a systematic procedure for simplifying matrices as well as a method for evaluating the determinant of a given square matrix. Subsequent chapters explore important numerical procedures, including the process for approximating characteristic roots and vectors plus direct and iterative methods for inverting matrices and solving systems of equations. Solutions to the problems are included. Read more