FiniteDimensional Vector Spaces: Second Edition (Dover Books on Mathematics)

A fine example of a great mathematicians 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 Its also extremely wellwritten 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 wellplaced 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 fr Mathematik.