This book begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. Material in this new edition has been rewritten and reorganized and new exercises have been added.
Author(s): Serge Lang
Series: Undergraduate Texts in Mathematics
Edition: 3rd
Publisher: Springer
Year: 2004
Language: English
Pages: 308
Cover......Page 1
Copyright......Page 5
Foreword......Page 6
Contents......Page 8
CHAPTER 1 Vector Spaces......Page 12
CHAPTER II Matrices......Page 34
CHAPTER III Linear Mappings......Page 54
CHAPTER IV Linear Maps and Matrices......Page 92
CHAPTER V Scalar Products and Orthogonal ity......Page 106
CHAPTER VI Determinants......Page 151
CHAPTER VII Symmetric, Hermitian, and Unitary Operators......Page 191
CHAPTER VIII Eigenvectors and Eigenvalues......Page 205
CHAPTER IX Polynomials and Matrices......Page 242
CHAPTER X Triangulation of Matrices and Linear Maps......Page 248
CHAPTER XI Polynomials and Primary Decomposition......Page 256
CHAPTER XII Convex Sets......Page 279
APPENDIX 1 Complex Numbers......Page 288
APPENDIX II Iwasawa Decomposition and Others......Page 294
Index......Page 304
