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Foundations of Linear and Generalized Linear Models
A valuable overview of the most important ideas and results in statistical modeling Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linearstatistical models.The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding. The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables.Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data.Focusing on the theoretical underpinnings of these models, Foundations ofLinear and Generalized Linear Models also features: An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methodsAn overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problemsNumerous examples that use R software for all text data analysesMore than 400 exercises for readers to practice and extend the theory, methods, and data analysisA supplementary website with datasets for the examples and exercises An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, Foundations of Linear and Generalized Linear Models is also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.
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Aegean Linear Script(s) : Rethinking the Relationship Between Linear A and Linear B
When does a continuum become a divide? This book investigates the genetic relationship between Linear A and Linear B, two Bronze Age scripts attested on Crete and Mainland Greece and understood to have developed one out of the other.By using an interdisciplinary methodology, this research integrates linguistic, epigraphic, palaeographic and archaeological evidence, and places the writing practice in its sociohistorical setting.By challenging traditional views, this work calls into question widespread assumptions and interpretative schemes on the relationship between these two scripts, and opens up new perspectives on the ideology associated with the retention, adaptation and transmission of a script, and how identity was negotiated at a moment of closer societal interaction between Cretans and Greek-speaking Mainlanders in the Late Bronze Age.By delving deeper into the structure and inner workings of these two writing systems, this book will make us rethink the relationship between Linear A and B.
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Linear Systems
This textbook provides a mathematical introduction to linear systems, with a focus on the continuous-time models that arise in engineering applications such as electrical circuits and signal processing.The book introduces linear systems via block diagrams and the theory of the Laplace transform, using basic complex analysis. The book mainly covers linear systems with finite-dimensional state spaces.Graphical methods such as Nyquist plots and Bode plots are presented alongside computational tools such as MATLAB.Multiple-input multiple-output (MIMO) systems, which arise in modern telecommunication devices, are discussed in detail.The book also introduces orthogonal polynomials with important examples in signal processing and wireless communication, such as Telatar’s model for multiple antenna transmission.One of the later chapters introduces infinite-dimensional Hilbert space as a state space, with the canonical model of a linear system.The final chapter covers modern applications to signal processing, Whittaker’s sampling theorem for band-limited functions, and Shannon’s wavelet. Based on courses given for many years to upper undergraduate mathematics students, the book provides a systematic, mathematical account of linear systems theory, and as such will also be useful for students and researchers in engineering.The prerequisites are basic linear algebra and complex analysis.
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Linear Algebra
Linear Algebra is intended for a one-term course at the junior or senior level.It begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorems for linear maps, including eigenvectors and eigenvalues, quadric and hermitian forms, diagonalization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form.The book also includes a useful chapter on convex sets and the finite-dimensional Krein-Milman theorem.The presentation is aimed at the student who has already had some exposure to the elementary theory of matrices, determinants, and linear maps.However, the book is logically self-contained. In this new edition, many parts of the book have been rewritten and reorganized, and new exercises have been added.
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Linear Algebra
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Linear Algebra
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Linear Algebra
This textbook invites readers to dive into the mathematical ideas of linear algebra.Offering a gradual yet rigorous introduction, the author illuminates the structure, order, symmetry, and beauty of the topic.Opportunities to explore, master, and extend the theory abound, with generous exercise sets embodying the Hungarian tradition of active problem-solving.Determinants, matrices, and systems of linear equations begin the book.This unique ordering offers insights from determinants early on, while also admitting re-ordering if desired.Chapters on vector spaces, linear maps, and eigenvalues and eigenvectors follow.Bilinear functions and Euclidean spaces build on the foundations laid in the first half of the book to round out the core material.Applications in combinatorics include Hilbert's third problem, Oddtown and Eventown problems, and Sidon sets, a favorite of Paul Erdos.Coding theory applications include error-correction, linear, Hamming, and BCH codes.An appendix covers the algebraic basics used in the text. Ideal for students majoring in mathematics and computer science, this textbook promotes a deep and versatile understanding of linear algebra.Familiarity with mathematical proof is assumed, though no prior knowledge of linear algebra is needed.Supplementary electronic materials support teaching and learning, with selected answers, hints, and solutions, and an additional problem bank for instructors.
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Similar search terms for Linear:
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Is it linear or non-linear?
The relationship between the variables is non-linear.
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What is the difference between a linear term, a linear equation, and a linear function?
A linear term is a single variable or constant raised to the power of 1, such as 3x or 5. A linear equation is an equation that can be written in the form y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope, and b is the y-intercept. A linear function is a mathematical relationship between two variables that can be represented by a straight line on a graph, and it can be expressed in the form f(x) = mx + b, where f(x) represents the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.
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What is the linear span of a linear space?
The linear span of a linear space is the set of all possible linear combinations of the vectors in that space. In other words, it is the collection of all possible vectors that can be obtained by scaling and adding the vectors in the space. The linear span forms a subspace of the original space and is often used to describe the "space" that is covered by the original set of vectors. It is a fundamental concept in linear algebra and is used to understand the properties and structure of vector spaces.
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Is my proof on linear independence in linear algebra correct?
To provide accurate feedback on the correctness of your proof on linear independence in linear algebra, I would need to review the specific details and steps of your proof. Please share your proof or key arguments so that I can assess its validity and provide you with constructive feedback.
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Is my proof about linear independence in linear algebra correct?
To provide an accurate assessment of your proof, I would need to review the specific details and steps of your proof. Linear independence in linear algebra is a fundamental concept, and it is important to ensure that the proof is logically sound and follows the definitions and properties of linear independence. If you can provide the details of your proof, I would be happy to review it and provide feedback on its correctness.
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What is the difference between linear equations and linear functions?
Linear equations and linear functions are closely related, but there is a key difference between the two. A linear equation is a mathematical statement that two expressions are equal, typically in the form y = mx + b. On the other hand, a linear function is a mathematical relationship between an independent variable and a dependent variable, typically in the form f(x) = mx + b. In other words, a linear equation is a specific instance of a linear function, where the equation represents the relationship between the variables.
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What is the connection between linear algebra and linear transformations?
Linear algebra is the branch of mathematics that deals with vector spaces and linear equations. Linear transformations are functions that preserve vector addition and scalar multiplication, which are fundamental concepts in linear algebra. Linear transformations can be represented by matrices, and studying linear algebra helps us understand the properties and behavior of linear transformations. In essence, linear algebra provides the tools and framework to analyze and manipulate linear transformations.
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What is the connection between linear algebra and linear mappings?
Linear algebra is the branch of mathematics that deals with vector spaces and linear transformations. Linear mappings are a fundamental concept in linear algebra, as they represent transformations that preserve the structure of vector spaces. Linear algebra provides the tools and techniques to study and analyze linear mappings, such as matrix representations, eigenvalues, and eigenvectors. Understanding linear algebra is essential for understanding the properties and behavior of linear mappings in various mathematical contexts.
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