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Lectures in Abstract Algebra: II. Linear Algebra: Graduate Texts in Mathematics, cartea 31

Autor N. Jacobson
en Limba Engleză Paperback – 15 ian 2013
The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presup­posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra. Our point of view in the present volume is basically the abstract conceptual one. However, from time to time we have deviated somewhat from this. Occasionally formal calculational methods yield sharper results. Moreover, the results of linear algebra are not an end in themselves but are essentialtools for use in other branches of mathematics and its applications. It is therefore useful to have at hand methods which are constructive and which can be applied in numerical problems. These methods sometimes necessitate a somewhat lengthier discussion but we have felt that their presentation is justified on the grounds indicated. A stu­ dent well versed in abstract algebra will undoubtedly observe short cuts. Some of these have been indicated in footnotes. We have included a large number of exercises in the text.
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Specificații

ISBN-13: 9781468470550
ISBN-10: 1468470558
Pagini: 296
Ilustrații: XII, 280 p.
Dimensiuni: 155 x 235 x 16 mm
Greutate: 0.42 kg
Ediția:1953
Editura: Springer
Colecția Springer
Seria Graduate Texts in Mathematics

Locul publicării:New York, NY, United States

Public țintă

Graduate

Cuprins

I: Finite Dimensional Vector Spaces.- II Linear Transformations.- III: The Theory of a Single Linear Transformation.- IV: Sets of Linear Transformations.- V: Bilinear Forms.- VI: Euclidean and Unitary Spaces.- VII: Products of Vector SpaÇes.- VIII: The Ring of Linear Transformations.- IX: Infinite Dimensional Vector Spaces.