Finite-Dimensional Vector Spaces - (Dover Books on Mathematics) by Paul R Halmos (Paperback)

About the Book

Classic, widely cited, and accessible treatment offers an ideal supplement to many traditional linear algebra texts. "Extremely well-written and logical, with short and elegant proofs." -- MAA Reviews. 1958 edition.

Book Synopsis

A fine example of a great mathematician's intellect and mathematical style, this classic on linear algebra is widely cited in the literature. The treatment is an ideal supplement to many traditional linear algebra texts and is accessible to undergraduates with some background in algebra.
"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.
"The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other 'modern' textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well-placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." -- Zentralblatt für Mathematik.

From the Back Cover

A fine example of a great mathematician's intellect and mathematical style, this classic on linear algebra is widely cited in the literature. The treatment is an ideal supplement to many traditional linear algebra texts and is accessible to undergraduates with some background in algebra.
"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.
"The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other 'modern' textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well-placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher."--Zentralblatt für Mathematik.
Dover (2017) republication of the edition originally published by D. Van Nostrand Co., Princeton, New Jersey, 1958.
www.doverpublications.com

About the Author

Hungarian-born Paul R. Halmos (1916-2006) established his reputation as a top-notch expositor of mathematics with this publication. He taught at the University of Chicago and the University of Michigan as well as other universities and made significant contributions to several areas of mathematics including mathematical logic, probability theory, ergodic theory, and functional analysis.