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Finite-Dimensional Vector Spaces

Paul R. Halmos
Publisher: 
Dover Publications
Publication Date: 
2017
Number of Pages: 
200
Format: 
Paperback
Price: 
14.95
ISBN: 
9780486814865
Category: 
Textbook
BLL Rating: 

The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Fernando Q. Gouvêa
, on
10/22/2017
]

See our review of the Springer edition. The book continues to be available from Springer, so the main advantage of this Dover reprint is the lower price.

This book helped create the discipline we now know as “linear algebra,” so it has great historical significance. Halmos based the book on lectures by John von Neumann, publishing it in the Annals of Mathematics Studies in 1942. The idea seems to have been to introduce students to Hilbert spaces and their operators by focusing on the finite-dimensional case. What was advanced mathematics in 1942 became a standard topic in the 1950s and entered the undergraduate curriculum, probably via the MAA recommendations, in the 1960s. 

The book certainly does not fit modern tastes, and it is hard to imagine a second-year undergraduate reading it with pleasure. It is nevertheless a great book, well suited for independent study.


Fernando Q. Gouvêa read this book as an undergraduate, but even in the 1970s it was not the official textbook. When he teaches Linear Algebra at Colby College, Fernando uses another textbook but wishes he could use this one.

The table of contents is not available.

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