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Linear Algebra Through Geometry (Undergraduate Texts in Mathematics) Hardcover – September 10, 1993

ISBN-13: 978-0387975863 ISBN-10: 0387975861 Edition: 2nd

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Product Details

  • Series: Undergraduate Texts in Mathematics
  • Hardcover: 308 pages
  • Publisher: Springer; 2nd edition (September 10, 1993)
  • Language: English
  • ISBN-10: 0387975861
  • ISBN-13: 978-0387975863
  • Product Dimensions: 6.1 x 0.8 x 9.2 inches
  • Shipping Weight: 1.3 pounds (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #908,367 in Books (See Top 100 in Books)

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16 of 16 people found the following review helpful By Nicholas Warren on July 21, 2005
Format: Hardcover Verified Purchase
A crystal clear book. It shows the geometrical significance of topics like eigenvalues/eigenvectors without losing the intuition in the formalism, like so many other books on Linear Algebra. The book would be particularly suitable for scientists, though prospective mathematicians would appreciate the "whys" too.

I only wish there were follow-on, more advanced, volumes!
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15 of 20 people found the following review helpful By Viktor Blasjo on October 6, 2007
Format: Hardcover
This is a very poorly written and highly opaque book. For example, chapter 2.7 (sic) is called "Classification of Conic Sections", but conic sections are not even mentioned until five pages into this 12-page chapter. Apparently, Banchoff and Wermer finds it appropriate that a reader who wants to learn about the classification of conic sections should be forced to wade through five pages of technicalities, including things like six exercises on computing powers of various matrices, without the slightest indication of what this has to do with the classification of conic sections. Another instance, one among many, where Banchoff and Wermer demonstrate their commitment to technical nonsense and aversion to broad understanding is chapter 2.5 on determinants. "The quantity ad-bc is called the determinant", etc., and then the opening paragraph ends "We shall see that the determinant gives us further information about the behaviour of A" (p. 61), and there follows a devastatingly boring and longwinded five-page discussion on the orientation of an ordered pair of vectors, which is a technicality that could and should be dismissed in one paragraph. Only after this do we see that determinants have to do with area, which is the defining geometric property of the determinant, and of enormous importance. Why not do it the other way around? Why not say straight away that determinants are areas and then deal with the technical matter of orientation and signed areas at the end of the section, instead of keeping the reader in the dark with the secretive and mysterious proclamation that the determinant "gives us further information about the behaviour of A"? Banchoff and Wermer also adhere to a most unfortunate dichotomy between two, three, and n dimensions, which makes the book clumsily structured and repetitive.Read more ›
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2 of 2 people found the following review helpful By TumericTJ on March 26, 2014
Format: Hardcover Verified Purchase
I fairly enjoyed this book, but didn't give it five stars because it was strongly disliked by the students I was assisting.
One the one hand, it is not so abstract as to pose a serious difficulty burden; on the other, it sometimes seemed to lack order or motivation.

I would recommend it as a supplementary text to a volume with more applications and easy-to-reference theorems, or to one that required more mathematical maturity.
Would be a good choice for the young or motivated self-learner: it reads like a novel.
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