This is the revised and expanded edition of the problem book Linear Algebra: Challenging Problems for Students, now entitled Problems in Linear Algebra and Matrix Theory. This new edition contains about fifty-five examples and many new problems, based on the author’s lecture notes of Advanced Linear Algebra classes at Nova Southeastern University (NSU-Florida) and short lectures Matrix Gems at Shanghai University and Beijing Normal University.The book is intended for upper division undergraduate and beginning graduate students, and it can be used as text or supplement for a second course in linear algebra. Each chapter starts with Definitions, Facts, and Examples, followed by problems. Hints and solutions to all problems are also provided.
Contents
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Frequently Used Notation
Frequently Used Theorems
Chapter 1 Vector Spaces
Chapter 2 Determinants, Inverses, Ranks, and Systems of Linear Equations
Chapter 3 Similarity, Eigenvalues, Matrix Decompositions, and Linear Transformations
Chapter 4 Special Matrices
Chapter 5 Inner Product Spaces
Chapter 6 Miscellaneous Problems
Hints and Answers for Chapter 1
Hints and Answers for Chapter 2
Hints and Answers for Chapter 3
Hints and Answers for Chapter 4
Hints and Answers for Chapter 5
Hints and Answers for Chapter 6
Notation
Main References
Postface – A Few Open Problems
Index