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Linear Algebra a Beginning Graduate Student Ought to Know

ISBN-10: 1402054947

ISBN-13: 9781402054945

Edition: 2nd 2007 (Revised)

Authors: Jonathan S. Golan

List price: $109.00
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Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of computational techniques. Unfortunately, in recent years the content of the linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or computational background. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the mathematics of the numerical algorithms they need for applications. Certainly, the material presented in the average undergraduate linear algebra course is insufficient for graduate study. This book is intended to fill this gap by providing enough material "theoretical and computational" to allow the student to work independently or in advanced courses. The book is intended to be used in one of several possible ways: (1) as a self-study guide ; (2) as a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level ; or (3) as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some basic ideas and techniques, such as the solution of a small system of linear equations over the real numbers. More importantly, it does assume a seriousness of purpose and a modicum of mathematical sophistication on the part of the reader. The book also containes over 1000 exercises, many of which are very challenging.
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Book details

List price: $109.00
Edition: 2nd
Copyright year: 2007
Publisher: Springer
Binding: Hardcover
Pages: 436
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 1.694
Language: English

Notation and terminology
Vector spaces over a field
Algebras over a field
Linear Dependence and Dimension
Linear Transformations
The endomorphism algebra of a vector space
Representation of linear transformations by matrices
The algebra of square matrices
Systems of linear equations
Eigenvalues and eigenvectors
Krylov subspaces
The dual space
Inner product spaces
Selfadjoint endomorphisms
Unitary and normal endomorphisms
Moore-Penrose pseudoinverses
Bilinear transformations and forms