A Guide to Advanced Linear Algebra

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MAA, Jul 7, 2011 - Mathematics - 251 pages
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Linear algebra occupies a central place in modern mathematics. This book provides a rigorous and thorough development of linear algebra at an advanced level. It approaches linear algebra from an algebraic point of view, but its selection of topics is governed not only for their importance in linear algebra itself, but also for their applications throughout mathematics. Topics treated in this book include: vector spaces and linear transformations; dimension counting and applications; representation of linear transformations by matrices; duality; determinants and their uses; rational and especially Jordan canonical form; bilinear forms; inner product spaces; normal linear transformations and the spectral theorem; and an introduction to matrix groups as Lie groups. Students in algebra, analysis and topology will all find much of interest and use to them and the careful treatment and breadth of subject matter will make this book a valuable reference for mathematicians throughout their professional lives.

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About the author (2011)

Steven H. Weintraub is Professor of Mathematics at Lehigh University. He was born in New York, received his undergraduate and graduate degrees from Princeton University, and was on the permanent faculty at Louisiana State University for many years before moving to Lehigh in 2001. He is the author of over 50 research papers, and this is his ninth book.

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