Lineare Algebra

Author: Gilbert Strang
Publisher: Springer-Verlag
ISBN: 3642556310
Format: PDF, ePub, Docs
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Diese Einführung in die lineare Algebra bietet einen sehr anschaulichen Zugang zum Thema. Die englische Originalausgabe wurde rasch zum Standardwerk in den Anfängerkursen des Massachusetts Institute of Technology sowie in vielen anderen nordamerikanischen Universitäten. Auch hierzulande ist dieses Buch als Grundstudiumsvorlesung für alle Studenten hervorragend lesbar. Darüber hinaus gibt es neue Impulse in der Mathematikausbildung und folgt dem Trend hin zu Anwendungen und Interdisziplinarität. Inhaltlich umfasst das Werk die Grundkenntnisse und die wichtigsten Anwendungen der linearen Algebra und eignet sich hervorragend für Studierende der Ingenieurwissenschaften, Naturwissenschaften, Mathematik und Informatik, die einen modernen Zugang zum Einsatz der linearen Algebra suchen. Ganz klar liegt hierbei der Schwerpunkt auf den Anwendungen, ohne dabei die mathematische Strenge zu vernachlässigen. Im Buch wird die jeweils zugrundeliegende Theorie mit zahlreichen Beispielen aus der Elektrotechnik, der Informatik, der Physik, Biologie und den Wirtschaftswissenschaften direkt verknüpft. Zahlreiche Aufgaben mit Lösungen runden das Werk ab.

Lineare Algebra

Author: Klaus Jänich
Publisher: Springer-Verlag
ISBN: 3662083809
Format: PDF
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"Daß ein Einführungstext zur Linearen Algebra bei der ständig wachsenden Flut von Lehrbüchern zu diesem weitgehend standardisierten Stoff überhaupt noch Besonderheiten bieten kann, ist gewiß bemerkenswert. Um so erstaunlicher, daß die hier schon beim ersten Durchblättern ins Auge springen... (Sie liegen in dem) im Kleindruck beigegebenen "Nebentext", in dem der Autor neben Beweisdetails vor allem "Erläuterungen, Motivation, gutes Zureden ", historische Hinweise und Aufmunterungen zum Lesen anderer Literatur untergebracht hat... Es wird all das Mehr wiedergegeben, das eine gute Vorlesung gegenüber einem Lehrbuch im üblichen Stil (Definition - Satz - Beweis - Beispiel) auszeichnet. Ein anderes charakteristisches Merkmal des Buches besteht in der Unterteilung in einen Kerntext, der die wichtigsten Sätze der Theorie enthält, und in Ergänzungen für Mathematiker und für Physiker. Am Ende jedes Paragraphen werden dem Erstsemesterstudenten neben Übungsmaterial auch einfache Testfragen angeboten, an denen er sein Verständnis erproben kann." Mathematisch-Physikalische-Semesterberichte

Linear Algebra

Author: Larry Smith
Publisher: Springer Science & Business Media
ISBN: 9780387984551
Format: PDF, Docs
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This popular and successful text was originally written for a one-semester course in linear algebra at the sophomore undergraduate level. Consequently, the book deals almost exclusively with real finite dimensional vector spaces, but in a setting and formulation that permits easy generalisation to abstract vector spaces. A wide selection of examples of vector spaces and linear transformation is presented to serve as a testing ground for the theory. In the second edition, a new chapter on Jordan normal form was added which reappears here in expanded form as the second goal of this new edition, after the principal axis theorem. To achieve these goals in one semester it is necessary to follow a straight path, but this is compensated by a wide selection of examples and exercises. In addition, the author includes an introduction to invariant theory to show that linear algebra alone is incapable of solving these canonical forms problems. A compact, but mathematically clean introduction to linear algebra with particular emphasis on topics in abstract algebra, the theory of differential equations, and group representation theory.

Linear Algebra

Author: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 9780387964126
Format: PDF, ePub, Mobi
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"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 theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization 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.

Linear Algebra

Author: Charles Curtis
Publisher: Springer
ISBN: 0387909923
Format: PDF, ePub
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This revised and updated fourth edition designed for upper division courses in linear algebra includes the basic results on vector spaces over fields, determinants, the theory of a single linear transformation, and inner product spaces. While it does not presuppose an earlier course, many connections between linear algebra and calculus are worked into the discussion. A special feature is the inclusion of sections devoted to applications of linear algebra, which can either be part of a course, or used for independent study, and new to this edition is a section on analytic methods in matrix theory, with applications to Markov chains in probability theory. Proofs of all the main theorems are included, and are presented on an equal footing with methods for solving numerical problems. Worked examples are integrated into almost every section, to bring out the meaning of the theorems, and illustrate techniques for solving problems. Many numerical exercises make use of all the ideas, and develop computational skills, while exercises of a theoretical nature provide opportunities for students to discover for themselves.

Introduction to Linear Algebra

Author: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 1461210704
Format: PDF, ePub
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This is a short text in linear algebra, intended for a one-term course. In the first chapter, Lang discusses the relation between the geometry and the algebra underlying the subject, and gives concrete examples of the notions which appear later in the book. He then starts with a discussion of linear equations, matrices and Gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, while others are conceptual.

Lineare Algebra

Author: Gerd Fischer
Publisher: Springer-Verlag
ISBN: 3658039450
Format: PDF
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Das seit über 30 Jahren bewährte, einführende Lehrbuch eignet sich als Grundlage für eine zweisemestrige Vorlesung für Studierende der Mathematik, Physik und Informatik. Für einen schnellen und leichteren Einstieg ist das Buch ebenfalls zu verwenden, indem die markierten Abschnitte weggelassen werden. Zentrale Themen sind: Lineare Gleichungssysteme, Eigenwerte und Skalarprodukte. Besonderer Wert wird darauf gelegt, Begriffe zu motivieren, durch Beispiele und durch Bilder zu illustrieren und konkrete Rechenverfahren für die Praxis abzuleiten. Der Text enthält zahlreiche Übungsaufgaben. Lösungen dazu findet man in dem von H. Stoppel und B. Griese verfassten "Übungsbuch zur Linearen Algebra ". Zur Motivation der Studierenden enthält das Buch eine Einführung, in der die Bedeutung der Linearen Algebra als Grundlage innerhalb der Mathematik und ihren Anwendungen beschrieben wird.

Linear Algebra

Author: Peter Petersen
Publisher: Springer Science & Business Media
ISBN: 1461436125
Format: PDF
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This textbook on linear algebra includes the key topics of the subject that most advanced undergraduates need to learn before entering graduate school. All the usual topics, such as complex vector spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form, and the rational canonical form, are covered, along with a chapter on determinants at the end of the book. In addition, there is material throughout the text on linear differential equations and how it integrates with all of the important concepts in linear algebra. This book has several distinguishing features that set it apart from other linear algebra texts. For example: Gaussian elimination is used as the key tool in getting at eigenvalues; it takes an essentially determinant-free approach to linear algebra; and systems of linear differential equations are used as frequent motivation for the reader. Another motivating aspect of the book is the excellent and engaging exercises that abound in this text. This textbook is written for an upper-division undergraduate course on Linear Algebra. The prerequisites for this book are a familiarity with basic matrix algebra and elementary calculus, although any student who is willing to think abstractly should not have too much difficulty in understanding this text.

Linear Algebra Done Right

Author: Sheldon Axler
Publisher: Springer
ISBN: 9780387982588
Format: PDF, Kindle
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This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on 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 has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, 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. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.