- Series: Undergraduate Texts in Mathematics
- Hardcover: 202 pages
- Publisher: Springer; 1st ed. 1958. Corr. 2nd printing 1993 edition (August 20, 1993)
- Language: English
- ISBN-10: 0387900934
- ISBN-13: 978-0387900933
- Product Dimensions: 6.1 x 0.5 x 9.2 inches
- Shipping Weight: 1.1 pounds (View shipping rates and policies)
- Average Customer Review: 3.8 out of 5 stars See all reviews (28 customer reviews)
- Amazon Best Sellers Rank: #1,211,394 in Books (See Top 100 in Books)
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Finite-Dimensional Vector Spaces (Undergraduate Texts in Mathematics) 1st ed. 1958. Corr. 2nd printing 1993 Edition
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“This is a classic but still useful introduction to modern linear algebra. It is primarily about linear transformations … . It’s also extremely well-written and logical, with short and elegant proofs. … The exercises are very good, and are a mixture of proof questions and concrete examples. The book ends with a few applications to analysis … and a brief summary of what is needed to extend this theory to Hilbert spaces.” (Allen Stenger, MAA Reviews, maa.org, May, 2016)
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Top customer reviews
However, the Martino Publishing edition (2012) in question is a reprint of the preliminary 1942 Princeton University Press edition. While of historical value, the typesetting of this text (done in typewriter) makes it a challenge to decipher. For instance, the Script and Fraktur letters are written in by hand!
If you are buying this for a class, this is definitely not the edition you are looking for!
I do not think this gap is really a fault of the author, than merely a reflection of the very different direction that the teaching undergraduate mathematics has taken since the author published this book. A much more accessible treatment of finite-dimensional spaces is "Linear Algebra Done Right" by Axler. Axler's book really does a much better job of helping a student of mathematics make the transition from "LA for engineers" to the LA of upper division math courses.
It is to LA as Rudin is to Analysis, or Spivak is to "Calculus on Manifolds"
I do love this book for its terseness. The subject is very well described, although I definitely think some subsections have no motivation. Lectures on Linear Algebra, is a good book to supplement for theoretical content.
Downsides: Terse, very little explanation. This is why I recommend (and use) this book as a reference. No solutions (I prefer it this way, but hints would be nice for some of the exercises).
Overall: The breadth of the material is simply incredible at such a great price. Halmos is a celebrated mathematician whose style is well worth studying. Perfect for advanced study / general linear algebra reference.