- Paperback: 196 pages
- Publisher: Princeton University Press; New edition edition (Jan 1 1947)
- Language: English
- ISBN-10: 0691090955
- ISBN-13: 978-0691090955
- Product Dimensions: 23 x 15 x 1.4 cm
- Shipping Weight: 322 g
- Average Customer Review: 4.0 out of 5 stars See all reviews (9 customer reviews)
- Amazon Bestsellers Rank: #2,013,706 in Books (See Top 100 in Books)
- See Complete Table of Contents
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Product Details |
Product Description
Review
“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
--This text refers to the
Hardcover
edition.
Book Description
As a newly minted Ph.D., Paul Halmos came to the Institute for Advanced Study in 1938--even though he did not have a fellowship--to study among the many giants of mathematics who had recently joined the faculty. He eventually became John von Neumann's research assistant, and it was one of von Neumann's inspiring lectures that spurred Halmos to write Finite Dimensional Vector Spaces. The book brought him instant fame as an expositor of mathematics.
Finite Dimensional Vector Spaces combines algebra and geometry to discuss the three-dimensional area where vectors can be plotted. The book broke ground as the first formal introduction to linear algebra, a branch of modern mathematics that studies vectors and vector spaces. The book continues to exert its influence sixty years after publication, as linear algebra is now widely used, not only in mathematics but also in the natural and social sciences, for studying such subjects as weather problems, traffic flow, electronic circuits, and population genetics.
In 1983 Halmos received the coveted Steele Prize for exposition from the American Mathematical Society for "his many graduate texts in mathematics dealing with finite dimensional vector spaces, measure theory, ergodic theory, and Hilbert space."
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First Sentence
In what follows we shall have occasion to use various classes of numbers (such as the class of all real numbers or the class of all complex numbers). Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
In what follows we shall have occasion to use various classes of numbers (such as the class of all real numbers or the class of all complex numbers). Read the first page
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Concordance
Browse Sample PagesConcordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Most helpful customer reviews
4.0 out of 5 stars
overrated, but still good,
By A Customer
This review is from: Finite-Dimensional Vector Spaces (Hardcover)
This book is a good reference, because it contains a lot more material than is contained in most courses, but I don't think I'd want to use it for an intro to linear algebra. It's got stuff that other books don't have, like Hilbert spaces & some analysis stuff in an appendix, tensor products, multilinear forms... It's good as a reference or supplement, but not as a main text, IMO. For an intro, I liked Axler's Linear Algebra Done Right or the Hoffman/Kunze book.
5.0 out of 5 stars
Linear algebra for mathematicians,
By
This review is from: Finite-Dimensional Vector Spaces (Hardcover)
I've just been looking on Amazon to see how some of my favorite old math texts are doing. I used this one about twenty years ago as a supplementary reference in a graduate course, and I still have my copy.Everybody with some mathematical background knows the name of Paul Richard Halmos. I saw him speak at Kent State University while I was an undergraduate there (some twenty-odd years ago); to this day I remember the sheer elegance of his presentation and even recall some of the specific points on which, like a magician, he drew gasps and applause from his audience of mathematicians and math students. This book displays the same elegance. If you're looking for a book that provides an exposition of linear algebra the way mathematicians think of it, this is it. This very fact will probably be a stumbling block for some readers. The difficulty is that, in order to appreciate what Halmos is up to here, you have to have _enough_ practice in mathematical thinking to grasp that linear algebra isn't the same thing as matrix algebra. In your introductory linear algebra course, linear transformations were probably simply identified with matrices. But really (i.e., mathematically), a linear transformation is a special sort of mathematical object, one that can be _represented_ by a matrix (actually by a lot of different matrices) once a coordinate system has been introduced, but one that 'lives' in the spaces with which abstract algebra deals, independently of any choice of coordinates. In short, don't expect numbers and calculations here. This book is about abstract algebraic structure, not about matrix computations. If that's not what you're looking for, you'll probably be disappointed in this book. If that _is_ what you want, you may still find this book hard going, but the rewards will be worth the effort.
5.0 out of 5 stars
The best abstract linear algebra book out there,
By Manfred Mann (Vienna, Austria) - See all my reviews
This review is from: Finite Dimensional Vector Spaces. (AM-7) (Paperback)
This book is the best if you are looking for an abstract approach to linear algebra. It provides elegant proofs to theorems that usually seem long-winded and awkward (like the cauchy-schwarz inequality). Sometimes in your lectures you may get to the point thinking "can't this be proven more elegant?" and you simply open halmos and it is there. Note that this book does not deal alot with matrices, everything of the theory is there, but you might miss illustrations and applications. In this case I recommend to back it up with Gilbert Strangs Linear Algebra and its Applications, which has an intuitive, matrice-oriented approach. Considering the price and the wide range of topics often left out in other books (like Nilpotence, Jordanform, Spectral Theorem,...) this simply is the one book you should buy and keep for reference.
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