文档介绍：THE LINEAR ALGEBRA A BEGINNING GRADUATE STUDENT
OUGHT TO KNOW
The Linear Algebra a Beginning
Graduate Student Ought to Know
Second Edition
by
JONATHAN S. GOLAN
University of Haifa, Israel
A . Catalogue record for this book is available from the Library of Congress.
ISBN-10 1-4020-5494-7 (PB)
ISBN-13 978-1-4020-5494-5 (PB)
ISBN-10 1-4020-5495-5 (e-book)
ISBN-13 978-1-4020-5495-2 (e-book)
Published by Springer,
. Box 17, 3300 AA Dordrecht, herlands.
Printed on acid-free paper
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© 2007 Springer
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To my grandsons: Shachar, Eitan, and Sarel
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Contents
1 Notation and terminology 1
2 Fields 5
3 Vectorspacesoverafield 17
4 Algebras over a field 33
5 Linear independence and dimension 49
6 Linear transformations 79
7 The endomorphism algebra of a vector space 99
8 Representation of linear transformations by matrices 117
9 The algebra of square matrices 131
10 Systems of linear equations 169
11 Determinants 199
12 Eigenvalues and eigenvectors 229
13 Krylov subspaces 267
vii
viii Contents
14 The dual space 285
15 Inner product spaces 299
16 Orthogonality 325
17 Selfadjoint Endomorphisms 349
18 Unitary and Normal endomorphisms 369
19 Moore-Penrose pseudoinverses 389
20 Bilinear transformations and forms 399
A Summary of Notation 423
Index 427
For whom is this book written?
Crow’s Law: Do not think what you want to think until you
know what you ought to
Linear algebra is a living, active branch of mathematical research which
is central to almost all other