Index of Definitions for Chapter 2
Auxiliary polynomial 132
Change of coordinate matrix 112
Clique 95
Coefficients of a differential equation 129
Coordinate function 120
Coordinate vector relative to a basis 80
Differential equation 129
Differential operator 131
Dimension theorem 70
Dominance relation 96
Double dual 120
Dual basis 121
Dual space 120
Euler’s formula 133
Exponential function 133
Fourier coefficient 119
Homogeneous linear differential equation 129
Identity matrix 82
Identity transformation 67
Incidence matrix 94
Inverse of a linear transformation 100
Inverse of a matrix 101
Invertible linear transformation 100
Invertible matrix 101
Isomorphic vector spaces 103
Isomorphism 103
Kronecker delta 82
Left-multiplication transformation 93
Linear functional 119
Linear operator 113
Linear transformation 65
Matrix representing a linear transformation 80
Nonhomogeneous differential equation 142
Nullity of a linear transformation 70
Null space 67
Ordered basis 79
Order of a differential equation 129
Order of a differential operator 131
Product of matrices 88
Projection on a subspace 76
Projection on the x-axis 66
Range 67
Rank of a linear transformation 70
Reflection about the x-axis 66
Rotation 66
Similar matrices 116
Solution to a differential equation 129
Solution space of a homogeneous differential equation 132
Standard ordered basis for 79
Standard ordered basis for 79
Standard representation of a vector space with respect to a basis 105
Transpose of a linear transformation 122
Zero transformation 67