Page 6 - Linear Algebra Done Right
P. 6
Contents
Preface to the Instructor ix
Preface to the Student xiii
Acknowledgments xv
Chapter 1
Vector Spaces 1
Complex Numbers .......................... 2
Definition of Vector Space ...................... 4
Properties of Vector Spaces ..................... 11
Subspaces ............................... 13
Sums and Direct Sums ........................ 14
Exercises ................................ 19
Chapter 2
Finite-Dimensional Vector Spaces 21
Span and Linear Independence ................... 22
Bases .................................. 27
Dimension ............................... 31
Exercises ................................ 35
Chapter 3
Linear Maps 37
Definitions and Examples ...................... 38
Null Spaces and Ranges ....................... 41
The Matrix of a Linear Map ..................... 48
Invertibility .............................. 53
Exercises ................................ 59
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