,LINEAR ALGEBRA
A Pathway to Abstract Mathematics
3rd Edition
G. Viglino
Ramapo College of New Jersey
January 2018
,
, Contents
CONTENTS
CHAPTER 1 MATRICES AND SYSTEMS OF LINEAR EQUATION
1.1 Systems of Linear Equations 1
1.2 Consistent and Inconsistent Systems of Equations 14
Chapter Summary 27
CHAPTER 2 VECTOR SPACES
2.1 Vectors in the plane, and Beyond 31
2.2 Abstract Vector Spaces 40
2.3 Properties of Vector Spaces 51
2.4 Subspaces 59
2.5 Lines and Planes 68
Chapter Summary 75
CHAPTER 3 BASES AND DIMENSION
3.1 Spanning Sets 77
3.2 Linear Independence 86
3.3 Bases 94
Chapter Summary 109
CHAPTER4 LINEARITY
4.1 Linear Transformations 111
4.2 Image and Kernel 124
4.3 Isomorphisms 135
Chapter Summary 149
CHAPTER 5 MATRICES AND LINEAR MAPS
5.1 Matrix Multiplication 151
5.2 Invertible Matrices 165
5.3 Matrix Representation of Linear Maps 178
5.4 Change of Basis 191
Chapter Summary 202
A Pathway to Abstract Mathematics
3rd Edition
G. Viglino
Ramapo College of New Jersey
January 2018
,
, Contents
CONTENTS
CHAPTER 1 MATRICES AND SYSTEMS OF LINEAR EQUATION
1.1 Systems of Linear Equations 1
1.2 Consistent and Inconsistent Systems of Equations 14
Chapter Summary 27
CHAPTER 2 VECTOR SPACES
2.1 Vectors in the plane, and Beyond 31
2.2 Abstract Vector Spaces 40
2.3 Properties of Vector Spaces 51
2.4 Subspaces 59
2.5 Lines and Planes 68
Chapter Summary 75
CHAPTER 3 BASES AND DIMENSION
3.1 Spanning Sets 77
3.2 Linear Independence 86
3.3 Bases 94
Chapter Summary 109
CHAPTER4 LINEARITY
4.1 Linear Transformations 111
4.2 Image and Kernel 124
4.3 Isomorphisms 135
Chapter Summary 149
CHAPTER 5 MATRICES AND LINEAR MAPS
5.1 Matrix Multiplication 151
5.2 Invertible Matrices 165
5.3 Matrix Representation of Linear Maps 178
5.4 Change of Basis 191
Chapter Summary 202
