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AuthorJacobson, Nathan. author
TitleLectures in Abstract Algebra [electronic resource] : II. Linear Algebra / by Nathan Jacobson
ImprintNew York, NY : Springer New York : Imprint: Springer, 1953
Connect tohttp://dx.doi.org/10.1007/978-1-4684-7053-6
Descript XII, 280 p. online resource

SUMMARY

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 presupยญ posed. 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 essential tools 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 stuยญ 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


CONTENT

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 Spaร{135}es -- VIII: The Ring of Linear Transformations -- IX: Infinite Dimensional Vector Spaces


Mathematics Matrix theory Algebra Mathematics Linear and Multilinear Algebras Matrix Theory



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