""Finite Dimensional Vector Spaces"" is a comprehensive and accessible textbook written by renowned mathematician Paul R. Halmos. The book is part of the ""University Series in Undergraduate Mathematics"" and is designed for undergraduate students who are studying linear algebra. The book covers the fundamental concepts of finite-dimensional vector spaces, including linear transformations, matrices, determinants, and eigenvalues. It also includes advanced topics such as inner product spaces, orthogonal projections, and the spectral theorem. The text is written in a clear and concise style, with numerous examples and exercises throughout to help students understand the material. Halmos also includes historical and philosophical remarks to provide context and motivation for the topics covered. Overall, ""Finite Dimensional Vector Spaces"" is an essential resource for any undergraduate student studying linear algebra or anyone interested in the mathematical foundations of vector spaces.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

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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)

“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 f�r Mathematik

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Finite Dimensional Vector Spaces: University Series in Undergraduate Mathematics

Halmos, Paul R

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