Lectures in Abstract Algebra : II. Linear Algebra / by N. Jacobson.

Format:

Book

Author/Creator:

Jacobson, Nathan, 1910-1999, author.

Contributor:

SpringerLink (Online service)

Series:

Graduate texts in mathematics 2197-5612 ; 31.

Graduate Texts in Mathematics, 2197-5612 ; 31

Language:

English

Subjects (All):

Matrices.

Algebra.

Linear and Multilinear Algebras, Matrix Theory.

Local Subjects:

Linear and Multilinear Algebras, Matrix Theory.

Physical Description:

1 online resource (XII, 280 pages).

Edition:

First edition 1953.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1953.

System Details:

text file PDF

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 presup-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 againches 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 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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9781468470536

Access Restriction:

Restricted for use by site license.