Applied Linear Algebra Class Time/Place: MWF 10:00am-10:50pm, CRUESS 107 Instructor: Jesus A. De Loera Office: 3228 Math. Building Email: [email protected] Office Hours: Monday 4:00pm-5:30pm, Friday 11am-12:30pm (or by special appointment). Please also use the online virtual office hours!! Via SMARTSITE discussion forum TA: Mr. Lang Mou Office: 2117 Math. Building Email: [email protected] Office Hours: Mondays 11am-12pm. Course Description: This course aims to help you develop a solid useful understanding of linear algebra, in particular focusing on applied and computational aspects of the subject. Linear algebra is truly important because linear equations and eigenvalue problems appear everywhere in engineering and science. A growing area of application is data-mining or analytics. This will be my favorite application during the course. Textbook: Matrix Methods in Data Mining and Pattern Recognition (Fundamentals of Algorithms), by Lars Elden, Published by SIAM ISBN-13: 9269 Note that this textbook has its official website:. Over there, you can find a lot of useful information. In particular, you should check out the currently known. ![]() Other useful references I use in class C. Moler: Numerical Computing with MATLAB by Cleve Moler, SIAM 2004 (available freely online) G. Strang: Linear Algebra and Its Applications, 4th Ed., Brooks/Cole, 2006. Shakiban: Applied Linear Algebra, Pearson, 2006. Meyer: Matrix Analysis and Applied Linear Algebra, SIAM, 2000. Here are the key topics: • Quick Review of Vector Spaces, Subspaces, Linear Independence, Bases, Rank, Linear Transformations, Determinants. Review of MATLAB. • LU decomposition and Linear system solving, basic of numerical analysis. • Norms, Inner Products, Orthogonal Bases, Gram-Schmidt Orthogonalization, QR Factorization • Projections, Least Squares Problems, Data Fitting/Regression • Eigenvalues, Eigenvectors, Diagonalization, Positive Definite Matrices • Range-Nullspace Decomposition, Singular Value Decomposition • Applications to Statistics & Data Analysis, Web Search Engines & Network problems, Information processing (signal & images, error-correcting codes), others. Prerequisite and Expectations • MAT 22A or MAT 67 (i.e., practical understanding of elementary linear algebra). • Basic knowledge of programming is required. Some experience in MATLAB is preferable, but MATLAB is very easy to learn. If you do not know how to use MATLAB, then you need to self-study using the MATLAB Primer and other material listed. ![]() • Formal attendance will not be taken. However, whether you are able to attend class or not, you are responsible for all the material presented in class. Note: The first 11 chapters, including the exercises, are now published as a self-contained textbook, Applied Linear Algebra, coauthored with Chehrzad Shakiban. • This is a 4 unit course! You are expected to work 3 hours at home for each hour of lecture. In other words, expect to have 10 hours of homework each week. Grading: The grades will be calculated using the average and standard deviation of the class. 100 points are possible which will be divided as follows: • Surprise quizzes online 10 points (about 7 quizzes of 2 points each, drop lowest scores, leaving top 5 scores) • Homeworks 20 points (5 homeworks of 5 points each, with the lowest score dropped), • Three midterm exams worth 20 points each (in class, Oct 24th, Nov 12, and Dec 10) with the lowest score dropped. Each exam will have 4 questions. • Final Project 25 points (Due December 19 at 12:30 pm) and • 3 points awarded for participation in class, office hours, or on the online discussion forum. • 2 points for the initial diagnostic exam Some important rules will be followed: • It is very important that you think and discuss the material, that is why I will give point for participation. Valuable contribution to the discussion be done online, in our forum at SMARTSITE, in class, or during office hours. • The SMARTSITE online forum is a great way for all of us to work, collaborate, and discuss what you are learning. If you have to enter formulas, you can most likely paste them in from MATLAB OR you can follow MATLAB's code notation to express equations. I will check the online discussion every morning and evening. Students should comment or make suggestions if you see how to help some else figure the problem, but DO NOT POST STRAIGHT SOLUTIONS! Give hints not answers! • The homework and other material will be posted at bottom of the course web site. Homework is due at the beginning of class on the day the assignment is due. LATE HOMEWORK WILL NOT BE ACCEPTED. • Your work is not being graded solely from the final answer, I expect you to write neatly, justify your reasoning and show all missing details. • Each time, a subset of three homework problems will be graded. You will loose a point automatically if you did not work out all problems. The lowest two homework scores will be dropped when assessing your grade. • I will assign some HW problems that require you to use MATLAB. • All exams are closed book. No calculators or cell phones allowed. • There will be NO MAKE-UP EXAMS but I will drop the lowest score. • The final project should be done in a team of 2 or 3 students. The project will include writing MATLAB code to investigate one of the application topics presented in class (see first lecture). More details and rules will be stated after the first midterm. This class uses MATLAB. You have several options for accessing it: • Create an account at the Math Department. Visit and follow the instructions. It is important to create your account before you come to the Lab for the first time. You can then work either at the Undergraduate Computer Lab (2118 Math. Bldg.) or from any other lab in the campus or even from your home PC by remotely connecting to one of the departmental servers, such as [point,cosine,sine,tangent].math.ucdavis.edu. The lab is open 9am-5pm on weekdays. • Use your own account at your own department if your department has the MATLAB license. This is the case for most of the engineering departments. • Buy a Student Version of MATLAB at UCD Bookstore (costs about $100). • Install Octave system on your own PC, which is free software and emulates MATLAB. Caution: Most likely you can do all the lab exercises, but I have not tested all the exercises yet. Visit the official web site of Octave at for downloading and installing information. For those who have never used MATLAB before or need to brush up their MATLAB knowledge, please take a look at the following highly useful MATLAB primers and tutorials. • The official is available from MATLAB (it is free, but registration of an account is required). • MATLAB offers a very nice online •. This publicly available version was written for older version of MATLAB 3.5, but still useful. (Our current version of MATLAB is 7.x.) •. This is the shortest one, tailored to the linear algebra context. This is a book by the creator of MATLAB. I highly recommend to read Chapter 1: Introduction to MATLAB as well as Chapter 2: Linear Equations, Chapter 5: Least Squares, and Chapter 10: Eigenvalues and Singular Values. VIDEO LECTURES TO REVIEW LINEAR ALGEBRA. Description: Read Now Matrix Analysis And Applied Linear Algebra by Carl D. Meyer and you can download with pub, pdf, txt, doc, and more file format with free account. Matrix analysis and applied linear algebra is an honest math text that circumvents the traditional definition-theorem-proof format that has bored students in the past. Meyer uses a fresh approach to introduce a variety of problems and examples ranging from the elementary to the challenging and from simple applications to discovery problems. The focus on applications is a big difference between this book and others. Meyer's book is more rigorous and goes into more depth than some. He includes some of the more contemporary topics of applied linear algebra which are not normally found in undergraduate textbooks. Modern concepts and notation are used to introduce the various aspects of linear equations, leading readers easily to numerical computations and applications. The theoretical developments are always accompanied with examples, which are worked out in detail. Each section ends with a large number of carefully chosen exercises from which the students can gain further insight. Description: Read Now Applied Linear Algebra by Lorenzo Adlai Sadun and you can download with pub, pdf, txt, doc, and more file format with free account. Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the decoupling principle. Traditionally, difference equations, markov chains, coupled oscillators, fourier series, the wave equation, the schrodinger equation, and fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to fourier series and the fourier transform. The second edition contains a series of explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises. Description: Read Now Applied Linear Algebra And Matrix Analysis by Thomas S. Shores and you can download with pub, pdf, txt, doc, and more file format with free account. This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, applied linear algebra and matrix analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises. Description: Read Now Applied Linear Algebra by CTI Reviews and you can download with pub, pdf, txt, doc, and more file format with free account. Facts101 is your complete guide to applied linear algebra. In this book, you will learn topics such as inner products and norms, minimization and least squares approximation, orthogonality, and equilibrium plus much more. With key features such as key terms, people and places, facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time. Description: Read Now Matrix Methods by Richard Bronson, Gabriel B. Costa and you can download with pub, pdf, txt, doc, and more file format with free account. Matrix methods: applied linear algebra, third edition, as a textbook, provides a unique and comprehensive balance between the theory and computation of matrices. The application of matrices is not just for mathematicians. The use by other disciplines has grown dramatically over the years in response to the rapid changes in technology. 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Balancing theoretical concepts with computational speed and accuracy, the book includes numerous short programs in matlab that can be used to solve problems involving systems of linear equations, matrices, vectors, computer graphics, and more. The book is accompanied by a cd-rom with all of the figures, m-files for all of the programs, and matlab simulations from industry. Complete solutions and microsoft powerpoint slides are available to instructors for use as a textbook. Description: Read Now Matrix Methods Applied Linear Algebra by CTI Reviews and you can download with pub, pdf, txt, doc, and more file format with free account. Facts101 is your complete guide to matrix methods, applied linear algebra. In this book, you will learn topics such as the inverse, an introduction to optimization, determinants, and eigenvalues and eigenvectors plus much more. 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