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An Introduction to the Theory of Linear Spaces (Dover Books on Mathematics), by Georgi E. Shilov, Richard A. Silverman
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This introduction to linear algebra and functional analysis offers a clear expository treatment, viewing algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. All abstract ideas receive a high degree of motivation, and numerous examples illustrate many different fields of mathematics. Abundant problems include hints or answers.
- Sales Rank: #1282360 in eBooks
- Published on: 2012-12-03
- Released on: 2012-12-03
- Format: Kindle eBook
Language Notes
Text: English, Russian (translation)
Most helpful customer reviews
3 of 3 people found the following review helpful.
Outstanding Contribution
By G. A. Schoenagel
Academician Shilov presents a synthesis of Algebra, Geometry and Analysis in exemplary treatment.
The text is quite lucid, as is expected from such an esteemed author.
The first chapter, Determinants, makes the topic as painless as possible (Smirnov does nicely in this regard,also).
Instead of decrying Determinants, why not understand them? This book is an opportunity to do just that.
Second Chapter, Linear Spaces, provides axiomatic development, with rather nice proofs.The text presses onward,
with the mandatory discussions of (among many other things) Linear Equations, Linear Functions and Quadratic Forms.
Three particularly noteworthy chapters are: Coordinate Transformations, Orthogonalization, and the last (long and superb) Infinite- Dimensional Euclidean Spaces.
The material throughout is coherently and lucidly displayed.
The problems are straightforward, some with hints, many with answers.
Proofs are understandable, examples are meaningful.
Indeed, this text is suitable for self-study (a stated aim of the author).
A fine achievement , worthy of serious study.
Highly Recommended.
3 of 4 people found the following review helpful.
Re-edit of "Linear Algebra"
By John Farnum
While the material in the book is good, it is just a reworking of Shilov's book "Linear Algebra,"
http://www.amazon.com/Linear-Algebra-Dover-Books-Mathematics/dp/048663518X/ref=sr_1_4?s=books&ie=UTF8&qid=1443805885&sr=1-4&keywords=linear+algebra
I got this one expecting to find additional insights and material and was disappointed to see that 80+% of the content is identical to the book I already own.
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