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CONTENTS
chapter 1 geometric vectors = 1
 1.1 Vectors in Elementary Science = 1
 1.2 Vectors in Plane Geometry = 6
 1.3 Vectors in Analytic Geometry = 12
 1.4 Isomorphism of the Two Vector Systems = 15
 1.5 The Dot Product = 21
 1.6 Some Analytic Vector Geometry = 27
 1.7 The Cross Product in 3-space = 34
 1.8 Lines and Planes = 39
chapter 2 matrices and linear equations = 47
 2.1 Matrices as Rectangular Arrays = 47
 2.2 Arithmetic of Matrices = 54
 2.3 Systems of Linear Equations:Gaussian Reduction = 60
 2.4 Solution by General Gaussian Reduction = 68
 2.5 Determinants = 75
 2.6 Solution of Linear Svstems: Cramer'a Rule = 82
chapter 3 real vector spaces = 91
 3.1 Real Vector Spaces = 91
 3.2 Subspacey = 97          
 3.3 Linear Dependence of Vectors = 101
 3.4 Basis and Dimension = 108
 3.5 Two Important Theorems = 110
chapter 4 linear transformations and matrices = 123
 4.1 Linear Transformations = 123
 4.2 Properties of Linear Transformations = 130
 4.3 Systems of Linear Transformations = 136
 4.4 Nonsingular Linear Transformations = 142
 4.5 Matrices of Linear Transformations = 150
 4.6  Matrices in Multiplicative Systems = 158
 4.7 Inversion of Matrices = 166
 4.8 Matrix Inversion by Gaussian Reduction = 173
chapter 5 inner product spaces = 181
 5.1 Euciidean Spaces = 181
 5.2 The Gram-Schmidt Process of Orthogonalization = 189
 5.3 Orthonormal Bases and Orthogonal Complements = 195
 5.4 Characteristic Values and Vectors = 201
 5.5 Change of Basis = 209
 5.6 Similarity and Diagonal Matrices = 217
 5.7 Geometry: Orthogonal Transformations = 225
 5.8 Geometry: Quadratic Forms = 235
 5.9 Geometry: Orthogonal Reduction of Quadratic Forms = 244
bibliography = 259
answers to most of the odd-numbered problems = 261
index = 271