Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Com este texto - breve, auto contido e preferencialmente dirigido a alunos que frequentem o 1º Ciclo em Economia ou Gestão - não pretendemos publicar outro (mais um ...) manual de Álgebra Linear, mas sim criar um instrumento de apoio para cursos que visem iniciar os estudantes no estudo desta disciplina. Assim, ao escrevê-lo tentámos observar algumas regras que nos parecem fundamentais: · Utilizar, apenas, a terminologia necessária, reconhecendo que nem todos pensam como um matemático; · Evitar confundir abordagem coerente e rigorosa com estudo exaustivo e completo, e, nesse sentido, substituir algumas das demonstrações mais exigentes por exemplos esclarecedores; · Assumir que os estudantes/leitores podem não estar familiarizados com o nosso vocabulário e que as palavras que utilizamos muitas vezes não significam o mesmo para os outros do que para nós. Por fim, esperamos que, também com estas lições, consigamos: · esclarecer os nossos alunos de que embora, nalgumas circunstâncias, a Matemática possa complicar e intimidar, ela é indispensável na decisão da escolha dos números, das relações ou associações que são fiáveis; · fazê-los sentir, simultaneamente, que o seu afastamento nos pode colocar em grande desvantagem quando nos dispomos a refletir sobre a multiplicidade de questões que surgem no nosso quotidiano. Este é, do nosso ponto de vista, o melhor caminho para os preparar para um futuro que se adivinha incerto e exigente.

Algebras, Linear. --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This unique and innovative book presents an exciting and complete detail of all the important topics related to the theory of square matrices of order 2. The readers exploring every detailed aspect of matrix theory are gently led toward understanding advanced topics. They will follow every notion of matrix theory with ease, accumulating a thorough understanding of algebraic and geometric aspects of matrices of order 2. The prime jewel of this book is its offering of an unusual collection of problems, theoretically motivated, most of which are new, original, and seeing the light of publication for the first time in the literature. Nearly all of the exercises are presented with detailed solutions and vary in difficulty from easy to more advanced. Many problems are particularly challenging. These, and not only these, invite the reader to unleash their creativity and research capabilities and to discover their own methods of attacking a problem. Matrices have a vast practical importance to mathematics, science, and engineering; therefore the readership of this book is intended to be broad: high school students wishing to learn the fundamentals of matrix theory, first year students who like to participate in mathematical competitions, graduate students who want to learn more about an application of a certain technique, doctoral students who are preparing for their prelim exams in linear algebra, and linear algebra instructors. Chapters 1–3 complement a standard linear algebra course. Pure and applied mathematicians who use matrix theory for their applications will find this book useful as a refresher. In fact, anyone who is willing to explore the methodologies discussed in this book and work through a collection of problems involving matrices of order 2 will be enriched.

Mathematics. --- Matrix theory. --- Algebra. --- Linear and Multilinear Algebras, Matrix Theory. --- Math --- Matrices. --- Algebras, Linear. --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Mathematics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book presents a modern and systematic approach to Linear Response Theory (LRT) by combining analytic and algebraic ideas. LRT is a tool to study systems that are driven out of equilibrium by external perturbations. In particular the reader is provided with a new and robust tool to implement LRT for a wide array of systems. The proposed formalism in fact applies to periodic and random systems in the discrete and the continuum. After a short introduction describing the structure of the book, its aim and motivation, the basic elements of the theory are presented in chapter 2. The mathematical framework of the theory is outlined in chapters 3–5: the relevant von Neumann algebras, noncommutative $L^p$- and Sobolev spaces are introduced; their construction is then made explicit for common physical systems; the notion of isopectral perturbations and the associated dynamics are studied. Chapter 6 is dedicated to the main results, proofs of the Kubo and Kubo-Streda formulas. The book closes with a chapter about possible future developments and applications of the theory to periodic light conductors. The book addresses a wide audience of mathematical physicists, focusing on the conceptual aspects rather than technical details and making algebraic methods accessible to analysts.

Physics. --- Functional analysis. --- Mathematical physics. --- Condensed matter. --- Mathematical Methods in Physics. --- Mathematical Physics. --- Condensed Matter Physics. --- Functional Analysis. --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Physical mathematics --- Physics --- Functional calculus --- Natural philosophy --- Philosophy, Natural --- Mathematics --- Calculus of variations --- Functional equations --- Integral equations --- Algebras, Linear. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Calculus of operations --- Line geometry --- Topology --- Liquids --- Matter --- Solids --- Physical sciences --- Dynamics