Linear Algebra Done Right


Author: Sheldon Axler
Publisher: Springer
ISBN: 3319110802
Category: Mathematics
Page: 340
View: 7894
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This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.

Flatland


Author: Edwin Abbott Abbott
Publisher: Bibebook
ISBN: 2824706775
Category: Fiction
Page: N.A
View: 3666
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Flatland est une allégorie, écrite en 1884, où l'auteur, Edwin Abbott Abbott, donne vie aux dimensions géométriques, le point, la ligne et les figures planes, avant d'en arriver à faire découvrir l'univers des volumes par un carré. Cette allégorie n'est pas sans rappeler la sortie de la caverne, voire le cheminement de Don Quichotte, l'hidalgo de Cervantes.

Linear Algebra and Its Applications


Author: Peter D. Lax
Publisher: John Wiley & Sons
ISBN: 1118626923
Category: Mathematics
Page: 392
View: 873
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Praise for the First Edition ". . .recommended for the teacher and researcher as well as forgraduate students. In fact, [it] has a place on everymathematician's bookshelf." -American Mathematical Monthly Linear Algebra and Its Applications, Second Edition presents linearalgebra as the theory and practice of linear spaces and linear mapswith a unique focus on the analytical aspects as well as thenumerous applications of the subject. In addition to thoroughcoverage of linear equations, matrices, vector spaces, game theory,and numerical analysis, the Second Edition featuresstudent-friendly additions that enhance the book's accessibility,including expanded topical coverage in the early chapters,additional exercises, and solutions to selected problems. Beginning chapters are devoted to the abstract structure of finitedimensional vector spaces, and subsequent chapters addressconvexity and the duality theorem as well as describe the basics ofnormed linear spaces and linear maps between normed spaces. Further updates and revisions have been included to reflect themost up-to-date coverage of the topic, including: The QR algorithm for finding the eigenvalues of a self-adjointmatrix The Householder algorithm for turning self-adjoint matricesinto tridiagonal form The compactness of the unit ball as a criterion of finitedimensionality of a normed linear space Additionally, eight new appendices have been added and cover topicssuch as: the Fast Fourier Transform; the spectral radius theorem;the Lorentz group; the compactness criterion for finitedimensionality; the characterization of commentators; proof ofLiapunov's stability criterion; the construction of the JordanCanonical form of matrices; and Carl Pearcy's elegant proof ofHalmos' conjecture about the numerical range of matrices. Clear, concise, and superbly organized, Linear Algebra and ItsApplications, Second Edition serves as an excellent text foradvanced undergraduate- and graduate-level courses in linearalgebra. Its comprehensive treatment of the subject also makes itan ideal reference or self-study for industry professionals.

Linear Algebra


Author: Belkacem Said-Houari
Publisher: Birkhäuser
ISBN: 3319637932
Category: Mathematics
Page: 384
View: 2798
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This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing the necessary concepts of eigenvalues and eigenvectors, as well as the theory of symmetric and orthogonal matrices. Each idea presented is followed by examples. The book includes a set of exercises at the end of each chapter, which have been carefully chosen to illustrate the main ideas. Some of them were taken (with some modifications) from recently published papers, and appear in a textbook for the first time. Detailed solutions are provided for every exercise, and these refer to the main theorems in the text when necessary, so students can see the tools used in the solution.

Linear algebra done right


Author: Sheldon Jay Axler
Publisher: N.A
ISBN: 9780387945965
Category: Mathematics
Page: 238
View: 5622
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This text for a second course in linear algebra is aimed at math majors and graduate students. The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents--without having defined determinants--a clean proof that every linear operator on a finite-dimensional complex vector space (or an odd-dimensional real vector space) has an eigenvalue. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus, the text starts by discussing vector spaces, linear independence, span, basis, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite-dimensional spectral theorem. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text.

Eléments d'Algèbre


Author: Leonhard Euler
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 4269
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Algèbre

Chapitre 9
Author: N. Bourbaki
Publisher: Springer
ISBN: 9783540353386
Category: Mathematics
Page: 208
View: 382
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Formes sesquilinéaires et formes quadratiques Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce neuvième chapitre du Livre d’Algèbre, deuxième Livre du traité, est consacré aux formes quadratiques, symplectiques ou hermitiennes et aux groupes associés. Il contient également une note historique. Ce volume est une réimpression de l’édition de 1959.

Algèbre: Les grands théorèmes


Author: Saunders Mac Lane,Garrett Birkhoff
Publisher: N.A
ISBN: N.A
Category: Algebra, Abstract
Page: N.A
View: 1557
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Gazette des mathématiciens


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 6552
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A Concise Introduction to Linear Algebra


Author: Géza Schay
Publisher: Springer Science & Business Media
ISBN: 0817683259
Category: Mathematics
Page: 330
View: 5602
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Building on the author's previous edition on the subject (Introduction to Linear Algebra, Jones & Bartlett, 1996), this book offers a refreshingly concise text suitable for a standard course in linear algebra, presenting a carefully selected array of essential topics that can be thoroughly covered in a single semester. Although the exposition generally falls in line with the material recommended by the Linear Algebra Curriculum Study Group, it notably deviates in providing an early emphasis on the geometric foundations of linear algebra. This gives students a more intuitive understanding of the subject and enables an easier grasp of more abstract concepts covered later in the course. The focus throughout is rooted in the mathematical fundamentals, but the text also investigates a number of interesting applications, including a section on computer graphics, a chapter on numerical methods, and many exercises and examples using MATLAB. Meanwhile, many visuals and problems (a complete solutions manual is available to instructors) are included to enhance and reinforce understanding throughout the book. Brief yet precise and rigorous, this work is an ideal choice for a one-semester course in linear algebra targeted primarily at math or physics majors. It is a valuable tool for any professor who teaches the subject.

Instabilités hydrodynamiques


Author: François Charru
Publisher: EDP Sciences
ISBN: 2759801101
Category: Science
Page: 408
View: 1333
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Depuis plus d'un siècle, les instabilités hydrodynamiques se révèlent un champ d'étude foisonnant et constamment renouvelé, enrichi par un dialogue fructueux de la mécanique avec de nombreuses branches de la physique, en particulier les transitions de phase, l'optique et la chimie non linéaires, l'astrophysique et la géophysique. Des problèmes anciens et fondamentaux comme la transition vers la turbulence sont vivifiés par de nouvelles idées. De nouveaux champs d'étude émergent aussi, comme le contrôle des instabilités, les fluides non newtoniens ou diphasiques, et les milieux granulaires. Cet ouvrage, issu d'un cours de Master de l'université de Toulouse, s'adresse à tout étudiant, chercheur ou ingénieur désirant s'initier à ces questions. Il est structuré par la théorie des systèmes dynamiques, des bifurcations et des ruptures de symétrie. Les phénomènes sont discutés, autant que possible, en termes d'échelles caractéristiques et d'analyse dimensionnelle pour accéder aux mécanismes physiques. Les méthodes asymptotiques ont aussi une large place. De nombreuses études expérimentales sont discutées en détail. Chaque chapitre se termine par des exercices, qui sont souvent des ouvertures vers des problèmes nouveaux. Enfin, onze notices biographiques présentent quelques grands noms attachés à l'étude des instabilités.

Géométrie projective


Author: Pierre Samuel
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: 176
View: 1428
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Issue des réflexions des peintres de la Renaissance sur la perspective, la géométrie projective s'est avérée, au début du XIXe siècle, être un outil unificateur de résultats géométriques disparates et un puissant moyen pour aller plus loin. A partir du milieu du XIXe siècle, la géométrie projective a été le fondement sur lequel s'est développée la géométrie algébrique. Dans le grand développement de celle-ci, jusqu'à l'époque contemporaine, les notions projectives y ont gardé une place de choix, notamment par le biais des systèmes linéaires. Partant d'un prérequis assez élémentaire d'algèbre, ce livre expose les fondements - tant algébriques qu'axiomatiques - de la géométrie algébrique et donne une grande place à leurs applications aux cercles, coniques et quadriques. A la portée des étudiants du premier cycle et des élèves des classes préparatoires, il est destiné à tous les amateurs de géométrie.

Calculus of Several Variables


Author: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 1461210682
Category: Mathematics
Page: 619
View: 1192
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This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.

Mathematical Reviews


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 9044
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Topologie générale


Author: Jacques Dixmier
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: 164
View: 7100
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Ce livre est un cours de topologie, destiné aux étudiants de deuxième cycle, première année (autrement dit, aux étudiants parvenus à leur troisième année d'université). Il a été enseigné à Paris VI en 1979-1980 pendant le premier semestre (3 heures hebdomadaires de cours, 4 heures hebdomadaires de travaux dirigés). La topologie est l'étude des notions de limite et de continuité, donc est en principe très ancienne. Toutefois, et sans vouloir remonter au Déluge, on peut trouver l'une des sources de la topologie moderne dans l'effort fait au dix-neuvième siècle pour mettre au point la théorie des fonctions de variable réelle. Les notions ainsi dégagées ont prouvé leur utilité dans un cadre bien plus vaste que celui des nombres réels ; c'est ce qui explique l'aspect très général des premières définitions. J'espère que l'abondance des exemples permettra au lecteur de ne pas perdre de vue l'aspect concret de la topologie ; après tout, il s'agit toujours, à certaines égards, de " géométrie ", et je ne saurais trop recommander à l'étudiant de garnir les marges de son livre de " figures " traduisant son intuition du sujet. On a signalé, par divers artifices typographiques, les théorèmes les plus importants, et les questions à la limite du " programme ". Quelques exercices ou problèmes terminent l'ouvrage.