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Linear Algebra for Economists
by Hasan Ersel Fuad Aleskerov Dmitri PiontkovskiThis textbook introduces students of economics to the fundamental notions and instruments in linear algebra. Linearity is used as a first approximation to many problems that are studied in different branches of science, including economics and other social sciences. Linear algebra is also the most suitable to teach students what proofs are and how to prove a statement. The proofs that are given in the text are relatively easy to understand and also endow the student with different ways of thinking in making proofs. Theorems for which no proofs are given in the book are illustrated via figures and examples. All notions are illustrated appealing to geometric intuition. The book provides a variety of economic examples using linear algebraic tools. It mainly addresses students in economics who need to build up skills in understanding mathematical reasoning. Students in mathematics and informatics may also be interested in learning about the use of mathematics in economics.
Linear Algebra for Physics
by Florian Scheck Nikolaos A. PapadopoulosThis textbook provides a full treatment of Linear Algebra devoted to undergraduate and graduate physics students. Although the mathematical level is similar to the corresponding mathematical textbooks in regard to definitions, propositions and proofs, it adopts a language and approach more attuned to the reader’s familiarity with physics lectures and physics textbooks. A distinctive feature is the emphasis placed on the significance of bases within a vector space. As a result, students gain a deeper understanding of how vector indices, despite their abundance, serve not as enemies but as friends since they give additional information about the mathematical objects being used, and facilitate access to tensor formalism. The book offers numerous worked examples and exercises with solution hints to deepen this knowledge.
Linear Algebra for the Sciences (UNITEXT #151)
by Thomas Kappeler Manuel BenzThis book is based on a course for first-semester science students, held by the second author at the University of Zurich several times. Its goal is threefold: to have students learn a minimal working knowledge of linear algebra, acquire some computational skills, and familiarize them with mathematical language to make mathematical literature more accessible. Therefore, we give precise definitions, introduce helpful notations, and state any results carefully worded. We provide no proofs of these results but typically illustrate them with numerous examples. Additionally, for better understanding, we often give supporting arguments for why they are valid.
Linear Algebra in Context: A Gateway to the Discrete Fourier Transform, Bilinear and Sesquilinear Forms, Algebras, Tensors and Mechanics (Springer Undergraduate Texts in Mathematics and Technology)
by Lawrence SusankaThis text combines a compact linear algebra course with a serious dip into various physical applications. It may be used as a primary text for a course in linear algebra or as a supplementary text for courses in applied math, scientific computation, mathematical physics, or engineering. The text is divided into two parts. Part 1 comprises a fairly standard presentation of linear algebra. Chapters 1–3 contain the core mathematical concepts typical for an introductory course while Chapter 4 contains numerous "short" applications. Chapter 5 is a repository of standard facts about matrix factorization and quadratic forms together with the "connective tissue" of topics needed for a coherent discussion, including the singular value decomposition, the Jordan normal form, Sylvester's law of inertia and the Witt theorems. Part I contains around 300 exercises, found throughout the text, and are an integral part of the presentation. Part 2 features deeper applications. Each of these "large" applications require no more than linear algebra to discuss, though the style and arrangement of results would be challenging to a beginning student and more appropriate for a second or later course. Chapter 6 provides an introduction to the discrete Fourier transform, including the fast Fourier algorithm. Chapter 7 is a thorough introduction to isometries and some of the classical groups, and how these groups have come to be important in physics. Chapter 8 is a fairly detailed look at real algebras and completes a presentation of the classical Lie groups and algebras. Chapter 9 is a careful discussion of tensors on a finite-dimensional vector space, finishing with the Hodge Star operator and the Grassmann algebra. Finally, Chapter 10 gives an introduction to classical mechanics including Noether's first theorem and emphasizes how the classical Lie groups, discussed in earlier chapters, become important in this setting. The Chapters of Part 2 are intended to give a sense of the ubiquity, of the indispensable utility, of linear algebra in modern science and mathematics and some feel for way it is actually used in disparate subject areas. Twelve appendices are included. The last seven refer to MATLAB® code which, though not required and rarely mentioned in the text, can be used to augment understanding. For example, fifty-five MATLAB functions implement every tensor operation from Chapter 9. A zipped file of all code is available for download from the author's website.
Linear Algebra in Data Science (Compact Textbooks in Mathematics)
by Peter Zizler Roberta La HayeThis textbook explores applications of linear algebra in data science at an introductory level, showing readers how the two are deeply connected. The authors accomplish this by offering exercises that escalate in complexity, many of which incorporate MATLAB. Practice projects appear as well for students to better understand the real-world applications of the material covered in a standard linear algebra course. Some topics covered include singular value decomposition, convolution, frequency filtering, and neural networks. Linear Algebra in Data Science is suitable as a supplement to a standard linear algebra course.
Linear Algebra over Commutative Rings
by Bernard R. McDonaldThis monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.
Linear Algebra to Differential Equations
by J. Vasundhara Devi Sadashiv G. Deo Ramakrishna KhandeparkarLinear Algebra to Differential Equations concentrates on the essential topics necessary for all engineering students in general and computer science branch students, in particular. Specifically, the topics dealt will help the reader in applying linear algebra as a tool. The advent of high-speed computers has paved the way for studying large systems of linear equations as well as large systems of linear differential equations. Along with the standard numerical methods, methods that curb the progress of error are given for solving linear systems of equations. The topics of linear algebra and differential equations are linked by Kronecker products and calculus of matrices. These topics are useful in dealing with linear systems of differential equations and matrix differential equations. Differential equations are treated in terms of vector and matrix differential systems, as they naturally arise while formulating practical problems. The essential concepts dealing with the solutions and their stability are briefly presented to motivate the reader towards further investigation. This book caters to the needs of Engineering students in general and in particular, to students of Computer Science & Engineering, Artificial Intelligence, Machine Learning and Robotics. Further, the book provides a quick and complete overview of linear algebra and introduces linear differential systems, serving the basic requirements of scientists and researchers in applied fields. Features Provides complete basic knowledge of the subject Exposes the necessary topics lucidly Introduces the abstraction and at the same time is down to earth Highlights numerical methods and approaches that are more useful Essential techniques like SVD and PCA are given Applications (both classical and novel) bring out similarities in various disciplines: Illustrative examples for every concept: A brief overview of techniques that hopefully serves the present and future needs of students and scientists.
Linear Algebra with Applications
by Jeffrey HoltPreparing you for conceptual thinking in an abstract setting. Linear Algebra with Applications, Second Edition, blends computational and conceptual topics throughout to prepare you for the rigors of conceptual thinking in an abstract setting. The early treatment of conceptual topics in the context of Euclidean space gives you more time, and a familiar setting, in which to absorb them. This organization also makes it possible to treat eigenvalues and eigenvectors earlier than in most texts. Abstract vector spaces are introduced later, once you have developed a solid conceptual foundation. Concepts and topics are frequently accompanied by applications to give you context and motivation. For those who learn best by example, Linear Algebra with Applications provides a large number of representative examples, over and above those used to introduce topics. The text also includes practice problems and over 2500 exercises, exposing you to computational and conceptual topics over a range of difficulty levels.
Linear Algebra with Applications (Second Edition)
by Jeffrey HoltHolt's Linear Algebra with Applications, Second Edition, blends computational and conceptual topics throughout to prepare students for the rigors of conceptual thinking in an abstract setting. The early treatment of conceptual topics in the context of Euclidean space gives students more time, and a familiar setting, in which to absorb them. This organization also makes it possible to treat eigenvalues and eigenvectors earlier than in most texts. Abstract vector spaces are introduced later, once students have developed a solid conceptual foundation. <p><p> Concepts and topics are frequently accompanied by applications to provide context and motivation. Because many students learn by example, Linear Algebra with Applications provides a large number of representative examples, over and above those used to introduce topics. The text also has over 2500 exercises, covering computational and conceptual topics over a range of difficulty levels.
Linear Algebra with Python: Theory and Applications (Springer Undergraduate Texts in Mathematics and Technology)
by Makoto Tsukada Yuji Kobayashi Hiroshi Kaneko Sin-Ei Takahasi Kiyoshi Shirayanagi Masato NoguchiThis textbook is for those who want to learn linear algebra from the basics. After a brief mathematical introduction, it provides the standard curriculum of linear algebra based on an abstract linear space. It covers, among other aspects: linear mappings and their matrix representations, basis, and dimension; matrix invariants, inner products, and norms; eigenvalues and eigenvectors; and Jordan normal forms. Detailed and self-contained proofs as well as descriptions are given for all theorems, formulas, and algorithms. A unified overview of linear structures is presented by developing linear algebra from the perspective of functional analysis. Advanced topics such as function space are taken up, along with Fourier analysis, the Perron–Frobenius theorem, linear differential equations, the state transition matrix and the generalized inverse matrix, singular value decomposition, tensor products, and linear regression models. These all provide a bridge to more specialized theories based on linear algebra in mathematics, physics, engineering, economics, and social sciences. Python is used throughout the book to explain linear algebra. Learning with Python interactively, readers will naturally become accustomed to Python coding. By using Python’s libraries NumPy, Matplotlib, VPython, and SymPy, readers can easily perform large-scale matrix calculations, visualization of calculation results, and symbolic computations. All the codes in this book can be executed on both Windows and macOS and also on Raspberry Pi.
Linear Algebra with its Applications (River Publishers Series in Mathematical, Statistical and Computational Modelling for Engineering)
by Ramakant MeherThis book contains a detailed discussion of the matrix operation, its properties, and its applications in finding the solution of linear equations and determinants. Linear algebra is a subject that has found the broadest range of applications in all branches of mathematics, physical and social sciences, and engineering. It has a more significant application in information sciences and control theory.A definition of linear algebra is that it is a part of algebra which is concerned with equations of the first degree. Thus, at the fundamental level, it involves the discussion of matrices and determinants, and the solutions of systems of linear equations, which have a wide application in further discussion of this subject.Technical topics discussed in the book include: Matrices Vector spaces Eigenvalue and eigenvectors Linear transformation Inner product spaces Diagonalizations Applications to conics and quadrics Canonical forms Least squares problems
Linear Algebra, Geometry and Transformation (Textbooks in Mathematics)
by Bruce SolomonThe Essentials of a First Linear Algebra Course and MoreLinear Algebra, Geometry and Transformation provides students with a solid geometric grasp of linear transformations. It stresses the linear case of the inverse function and rank theorems and gives a careful geometric treatment of the spectral theorem.An Engaging Treatment of the Interplay amo
Linear Algebra, Signal Processing, and Wavelets - A Unified Approach: MATLAB Version (Springer Undergraduate Texts in Mathematics and Technology)
by Øyvind RyanThis book offers a user friendly, hands-on, and systematic introduction to applied and computational harmonic analysis: to Fourier analysis, signal processing and wavelets; and to their interplay and applications. The approach is novel, and the book can be used in undergraduate courses, for example, following a first course in linear algebra, but is also suitable for use in graduate level courses. The book will benefit anyone with a basic background in linear algebra. It defines fundamental concepts in signal processing and wavelet theory, assuming only a familiarity with elementary linear algebra. No background in signal processing is needed. Additionally, the book demonstrates in detail why linear algebra is often the best way to go. Those with only a signal processing background are also introduced to the world of linear algebra, although a full course is recommended. The book comes in two versions: one based on MATLAB, and one on Python, demonstrating the feasibility and applications of both approaches. Most of the MATLAB code is available interactively. The applications mainly involve sound and images. The book also includes a rich set of exercises, many of which are of a computational nature.
Linear Algebra, Signal Processing, and Wavelets - A Unified Approach: Python Version (Springer Undergraduate Texts in Mathematics and Technology)
by Øyvind RyanThis book offers a user friendly, hands-on, and systematic introduction to applied and computational harmonic analysis: to Fourier analysis, signal processing and wavelets; and to their interplay and applications. The approach is novel, and the book can be used in undergraduate courses, for example, following a first course in linear algebra, but is also suitable for use in graduate level courses. The book will benefit anyone with a basic background in linear algebra. It defines fundamental concepts in signal processing and wavelet theory, assuming only a familiarity with elementary linear algebra. No background in signal processing is needed. Additionally, the book demonstrates in detail why linear algebra is often the best way to go. Those with only a signal processing background are also introduced to the world of linear algebra, although a full course is recommended.The book comes in two versions: one based on MATLAB, and one on Python, demonstrating the feasibility and applications of both approaches. Most of the code is available interactively. The applications mainly involve sound and images. The book also includes a rich set of exercises, many of which are of a computational nature.
Linear Algebra: A First Course with Applications (Textbooks in Mathematics)
by Larry E. KnopLinear Algebra: A First Course with Applications explores the fundamental ideas of linear algebra, including vector spaces, subspaces, basis, span, linear independence, linear transformation, eigenvalues, and eigenvectors, as well as a variety of applications, from inventories to graphics to Google's PageRank. Unlike other texts on the subject, thi
Linear Algebra: A Geometric Approach (Chapman Hall/crc Mathematics Ser. #7)
by E. SernesiThis is an undergraduate textbook suitable for linear algebra courses. This is the only textbook that develops the linear algebra hand-in-hand with the geometry of linear (or affine) spaces in such a way that the understanding of each reinforces the other. The text is divided into two parts: Part I is on linear algebra and affine geometry, finis
Linear Algebra: A Modern Introduction
by David PooleThis fourth edition emphasizes a vectors approach and better prepares students to make the transition from computational to theoretical mathematics. Balancing theory and applications, the book is written in a conversational style and combines a traditional presentation with a focus on student-centered learning. Theoretical, computational, and applied topics are presented in a flexible yet integrated way. Stressing geometric understanding before computational techniques, vectors and vector geometry are introduced early to help students visualize concepts and develop mathematical maturity for abstract thinking. Additionally, the book includes ample applications drawn from a variety of disciplines, which reinforce the fact that linear algebra is a valuable tool for modeling real-life problems.
Linear Algebra: An Inquiry-Based Approach (Textbooks in Mathematics)
by Jeff SuzukiLinear Algebra: An Inquiry-based Approach is written to give instructors a tool to teach students to develop a mathematical concept from first principles. The Inquiry-based Approach is central to this development. The text is organized around and offers the standard topics expected in a first undergraduate course in linear algebra. In our approach, students begin with a problem and develop the mathematics necessary to describe, solve, and generalize it. Thus students learn a vital skill for the 21st century: the ability to create a solution to a problem. This text is offered to foster an environment that supports the creative process. The twin goals of this textbook are: Providing opportunities to be creative, Teaching "ways of thinking" that will make it easier for to be creative. To motivate the development of the concepts and techniques of linear algebra, we include more than two hundred Activities on a wide range of problems, from purely mathematical questions, through applications in biology, computer science, cryptography, and more. Table of Contents Introduction and Features For the Student . . . and Teacher Prerequisites Suggested Sequences 1. Tuples and Vectors 2. Systems of Linear Equations 3. Transformations 4. Matrix Algebra 5. Vector Spaces 6. Determinants 7. Eigenvalues and Eigenvectors 8. Decomposition 9. Extras Bibliography Index Bibliography Jeff Suzuki is Associate Professor of Mathematics at Brooklyn College and holds a Ph.D. from Boston University. His research interests include mathematics education, history of mathematics, and the application of mathematics to society and technology. He is a two-time winner of the prestigious Carl B. Allendoerfer Award for expository writing. His publications have appeared in The College Mathematics Journals; Mathematics Magazine; Mathematics Teacher; and the American Mathematical Society's blog on teaching and learning mathematics. His YouTube channel (http://youtube.com/jeffsuzuki1) includes videos on mathematical subjects ranging from elementary arithmetic to linear algebra, cryptography, and differential equations.
Linear Algebra: Concepts and Methods
by Martin Anthony Michele HarveyAny student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the fundamental topics. The book is ideal as a course text or for self-study. Instructors can draw on the many examples and exercises to supplement their own assignments. End-of-chapter sections summarise the material to help students consolidate their learning as they progress through the book.
Linear Algebra: Ideas and Applications
by Richard C. PenneyPraise for the Third Edition "This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications." - Electric Review Learn foundational and advanced topics in linear algebra with this concise and approachable resource A comprehensive introduction, Linear Algebra: Ideas and Applications, Fifth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique. The book introduces each new concept in the context of explicit numerical examples, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs. Linear Algebra: Ideas and Applications, Fifth Edition also features: A new application section on section on Google’s Page Rank Algorithm. A new application section on pricing long term health insurance at a Continuing Care Retirement Community (CCRC). Many other illuminating applications of linear algebra with self-study questions for additional study. End-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material Numerous computer exercises throughout using MATLAB® code Linear Algebra: Ideas and Applications, Fifth Edition is an excellent undergraduate-level textbook for one or two semester undergraduate courses in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.
Linear Algebra: Key Ideas and Methods for a First Course (Synthesis Lectures on Mathematics & Statistics)
by Haiyan TianThis book presents algebra in a concise and clear way, allowing beginner students to quickly attain the required proficiency. As to opposed to existing books on the subject that cover too many topics, some of which are too complex and intimidating for a first course in linear algebra, this book only presents the essential topics in a more user-friendly manner. The author includes an optimized order of topics that are adapted to the learning patterns of students. In addition, carefully designed examples are presented to enhance reader confidence to master the material and to avoid frequently observed frustration. This textbook is ideal for a one semester course on basic linear algebra for college students majoring in mathematics, engineering, and other sciences.
Linear Algebra: What you Need to Know (Textbooks in Mathematics)
by Hugo J. WoerdemanThis 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.
Linear Canonical Transforms
by John J. Healy M. Alper Kutay Haldun M. Ozaktas John T. SheridanThis book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.
Linear Differential Equations and Oscillators (Mathematics and Physics for Science and Technology)
by Luis Manuel Braga da Costa CamposLinear Differential Equations and Oscillators is the first book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This first book consists of chapters 1 and 2 of the fourth volume. The first chapter covers linear differential equations of any order whose unforced solution can be obtained from the roots of a characteristic polynomial, namely those: (i) with constant coefficients; (ii) with homogeneous power coefficients with the exponent equal to the order of derivation. The method of characteristic polynomials is also applied to (iii) linear finite difference equations of any order with constant coefficients. The unforced and forced solutions of (i,ii,iii) are examples of some general properties of ordinary differential equations. The second chapter applies the theory of the first chapter to linear second-order oscillators with one degree-of-freedom, such as the mechanical mass-damper-spring-force system and the electrical self-resistor-capacitor-battery circuit. In both cases are treated free undamped, damped, and amplified oscillations; also forced oscillations including beats, resonance, discrete and continuous spectra, and impulsive inputs. Describes general properties of differential and finite difference equations, with focus on linear equations and constant and some power coefficients Presents particular and general solutions for all cases of differential and finite difference equations Provides complete solutions for many cases of forcing including resonant cases Discusses applications to linear second-order mechanical and electrical oscillators with damping Provides solutions with forcing including resonance using the characteristic polynomial, Green' s functions, trigonometrical series, Fourier integrals and Laplace transforms
Linear Differential Equations in the Complex Domain: From Classical Theory to Forefront (Lecture Notes in Mathematics #2271)
by Yoshishige HaraokaThis book provides a detailed introduction to recent developments in the theory of linear differential systems and integrable total differential systems. Starting from the basic theory of linear ordinary differential equations and integrable systems, it proceeds to describe Katz theory and its applications, extending it to the case of several variables. In addition, connection problems, deformation theory, and the theory of integral representations are comprehensively covered. Complete proofs are given, offering the reader a precise account of the classical and modern theory of linear differential equations in the complex domain, including an exposition of Pfaffian systems and their monodromy problems. The prerequisites are a course in complex analysis and the basics of differential equations, topology and differential geometry. This book will be useful for graduate students, specialists in differential equations, and for non-specialists who want to use differential equations.