Ebook: Lectures in Abstract Algebra: II. Linear Algebra
Author: Nathan Jacobson (auth.)
- Tags: Mathematics general
- Series: Graduate Texts in Mathematics 31
- Year: 1953
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
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 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 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.
Content:
Front Matter....Pages i-xii
Finite Dimensional Vector Spaces....Pages 1-30
Linear Transformations....Pages 31-62
The Theory of a Single Linear Transformation....Pages 63-114
Sets of Linear Transformations....Pages 115-135
Bilinear Forms....Pages 136-171
Euclidean and Unitary Spaces....Pages 172-198
Products of Vector Spaces....Pages 199-226
The Ring of Linear Transformations....Pages 227-237
Infinite Dimensional Vector Spaces....Pages 238-276
Back Matter....Pages 277-280
Content:
Front Matter....Pages i-xii
Finite Dimensional Vector Spaces....Pages 1-30
Linear Transformations....Pages 31-62
The Theory of a Single Linear Transformation....Pages 63-114
Sets of Linear Transformations....Pages 115-135
Bilinear Forms....Pages 136-171
Euclidean and Unitary Spaces....Pages 172-198
Products of Vector Spaces....Pages 199-226
The Ring of Linear Transformations....Pages 227-237
Infinite Dimensional Vector Spaces....Pages 238-276
Back Matter....Pages 277-280
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