To browse Academia. Skip to main content. Log In Sign Up. Serge Lang Introduction to Linear Algebra. Pranav Thakkar. Axler F. Gehring K. Editorial Board S. MI U. Undergraduate texts in mathematics Includes index. Algebras, Linear. L37 '. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher Springer-Verlag, Fifth Avenue, New York, New YorkU.
Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc. Except for an occasional example or exercise the text is logically independent of calculus, and could be taught early.
In practice, I expect it to be used mostly for students who have had two or three terms of calculus. The course could also be given simultaneously with, or im- mediately after, the first course in calculus. I have included some examples concerning vector spaces of functions, but these could be omitted throughout without impairing the under- standing of the rest of the book, for those who wish to concentrate exclusively on euclidean space. The first chapter is designed to serve several purposes.
First, and most basically, it establishes the fundamental connection between linear algebra and geometric intuition.Best Book of Modern Algebra
There are indeed two aspects at least to linear algebra: the formal manipulative aspect of computations with matrices, and the geometric interpretation. I do not wish to prejudice one in favor of the other, and I believe that grounding formal manipula- tions in geometric contexts gives a very valuable background for those who use linear algebra. Second, this first chapter gives immediately concrete examples, with coordinates, for linear combinations, perpendicu- larity, and other notions developed later in the book.
Thus the first chapter gives a quick overview of many topics in the book. The content of the first chapter is also the most fundamental part of what is used in calculus courses concerning functions of several variables, which can do a lot of things without the more general ma- trices.Maggiori informazioni sull'abbonamento a Scribd Home.
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Contrassegna per contenuti inappropriati. Scarica ora. Titoli correlati. Carosello precedente Carosello successivo. Rosa L. Salta alla pagina. Cerca all'interno del documento. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, with: our the prior wntten permission of the publisher. Enough material has been included for a one-year course, but by suitable omissions, it will also be easy to use the book for one term.
During the past decade, the curriculum for algebra courses at the under- graduate level has shifted its emphasis towards linear algebra. The shift is partly due to the recognition that this part of algebra is easier to under- stand than some other parts being less abstract, and in any case being directly motivated by spatial geometryand partly because of the wide applications which exist for linear algebra.
Consequently, I have started the book with the basic notion of vector in real Euclidean space, which sets the general pattern for much that follows. The chapters on groups and rings are included because of their important relation to the linear algebra, the group of invertible linear maps or matrices and the ring of linear maps of a vector space being perhaps the most striking examples of groups and rings.
The fact that a vector space over a field can be viewed fruitfully as a module over its ring of endomorphisms is worth emphasizing as part of a linear algebra course, However, because of the general intent of the book, these chapters are not treated with quite the same degree of completeness which they might otherwise receive, and a short text on basic algebraic structures groups, rings, fields, sets, etc.
The tensor product, and especially the alternating product, are so im- portant in courses in advanced calculus that it was imperative to insert a chapter on them, keeping the applications in mind.Nokia ta 1124 hard reset
The limited purpose of the chapter here allows for concreteness and simplicity. The appendix on convex sets pursues some of the geometric ideas of Chapter I, taking for granted some standard facts about continuous fune- tions on compact sets, closures of sets, etc. It can essentially be read after Chapter I, and after knowing the definition of a linear map. Various odds and ends are given in a second appendix including a proof of the algebraic closure of the complex numberswhich can be covered according to the judgement of the instructor.
For instance, we take vector spaces over the reals, we consider only the positive definite sealar product, we omit the dual space, ete. Of course, better students can handle the more complete book at once, but I hope that the separation will be pedagogically useful for others. In this second edition, I have rewritten a few sections, and inserted a few new topics. I have also added many new exercises. Definition of points in n-space Located veetors.The publisher has supplied this book in DRM Free form with digital watermarking.
The publisher has supplied this book in encrypted form, which means that you need to install free software in order to unlock and read it. To read this ebook on a mobile device phone or tablet you'll need to install one of these free apps:. The publisher has set limits on how much of this ebook you may print or copy. See details. Toggle navigation. New to eBooks. Introduction to Linear Algebra 2nd ed. Serge Lang. This title will be released on. This eBook is no longer available for sale.
This eBook is not available in your country. 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. In The Press. About The Author.Browning cynergy sporting
Customer Reviews. Digital Rights Management DRM The publisher has supplied this book in encrypted form, which means that you need to install free software in order to unlock and read it. It's not the same as Adobe Reader, which you probably already have on your computer.
Limits on printing and copying The publisher has set limits on how much of this ebook you may print or copy. How many copies would you like to buy?A word in response to the corona virus crisis: Your print orders will be fulfilled, even in these challenging times. 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.
It begins with an exposition of the basic theory of finite-dimensional vector spaces and proceeds to explain the structure theorems for linear maps, including eigenvectors and eigenvalues, quadratic and Hermitian forms, diagonalization of symmetric, Hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form.
Mathematics Algebra. Undergraduate Texts in Mathematics Free Preview. Buy eBook. Buy Hardcover. Buy Softcover. FAQ Policy. About this Textbook Linear Algebra is intended for a one-term course at the junior or senior level.
Matrices Pages Lang, Serge. Linear Mappings Pages Lang, Serge. Determinants Pages Lang, Serge. Eigenvectors and Eigenvalues Pages Lang, Serge. Polynomials and Matrices Pages Lang, Serge. Convex Sets Pages Lang, Serge.How to tell a rooster from a hen chick
It only takes a minute to sign up. I am self learning abstract algebra. I am using the book Algebra by Serge Lang. The book has different definitions for some algebraic structures.Legend of the phoenix drama recap
For example, according to that book rings are defined to have multiplicative identities. Also modules are defined slightly differently Lang 's " Algebra " is without doubt one of the classic references but sticking to it, or to only one book for that matter, depends highly on your style tastes, background level and aim. You should check out other standard references listed below, and see their style to decide which suits you best:. It is filled with lots of exercises and examples.
The third book is very abstract and general, encyclopedic and good as a reference since it is highly formally organized with just definitions-theorems-proofs-corollaries, with a great selection of exercises I think better than Lang's ; but, although it covers with great generality topics the others take longer to explain, it lacks chapters on homological algebra or representations, which the others have. Finally the second book is a mixture of all styles, and in particular is my favourite.
It is the biggest, with around pages, it has an informal style in its explanations but a highly rigorous development, with insightful examples and filled also with lots of exercises which I particularly find well-suited for self-study. The last one is a quite recent textbook which some people will detest while others will love. There are many other abstract algebra titles, this is just a small standard selection. Once you have mastered the standard graduate course, or if you want to deepen your knowledge on particular chapters of the previous books, like commutative algebra for example as requisite for algebraic geometry, you may jump to the next level of more specialized texts:.
In addition to the other wonderful responses, you might want a very accessible and gentle introduction. At my university, we used John B.
It assumes very little and contains a lot of exercises.
If you a little more conceptual approach and don't mind reading a lotyou could check out Paolo Aluffi's "Algebra: Chapter 0". If you're happy with Lang's Algebrait's a fine book to stick with. It is very intuitive, it has great exercises that help build competency with proofs, and the exercises are organized according to level of difficulty, beginning, e.
In that sense, it is very developmental in its structure. The other thing worth noting is that it is "group" oriented. One text that has not yet been mentioned yet is Michael Artin's Algebra, 2nd ed.Skip to main content Skip to table of contents. Advertisement Hide.
Download book PDF. Front Matter Pages i-xv.Cl7 tsx
Front Matter Pages Pages Algebraic Extensions. Galois Theory. Extensions of Rings. Transcendental Extensions. Algebraic Spaces.
Introduction to Linear Algebra (2nd ed.)
Noetherian Rings and Modules. Real Fields. Absolute Values. Matrices and Linear Maps. Representation of One Endomorphism. Structure of Bilinear Forms. The Tensor Product.
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Representations of Finite Groups. The Alternating Product. General Homology Theory. Finite Free Resolutions. Back Matter Pages About this book Introduction This book is intended as a basic text for a one-year course in Algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra.
It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text. Comments on Serge Lang's Algebra: Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books.
Steele Prize for Mathematical Exposition for his many mathematics books. The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra. MathSciNet's review of the first edition.Our goal is to provide high-quality video, TV streams, music, software, documents or any other shared files for free!
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