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AppendixCNotation

The following table defines the notation used in this book. Page numbers or references refer to the first appearance of each symbol.

Symbol Description Location
0 The number zero Paragraph
R The real numbers Paragraph
Rn Real n -space Definition
A12B A vector Paragraph
0 The zero vector Paragraph
Span{v1,v2,...,vk} Span of vectors Definition
{x|condition} Set builder notation Note
Ri Row i of a matrix Item
m×nmatrix Size of a matrix Important Note
Col(A) Column space Definition
Nul(A) Null space Definition
dimV Dimension of a subspace Definition
rank(A) The rank of a matrix Definition
nullity(A) The nullity of a matrix Definition
T:Rn→Rm transformation with domain Rn and codomain Rm Definition
IdRn Identity transformation Definition
rank(T) The rank of a linear transformation Definition
nullity(T) The nullity of a linear transformation Definition
e1,e2,... Standard coordinate vectors Notation
In n×n identity matrix Definition
aij The i,j entry of a matrix Notation
0 The zero transformation Paragraph
0 The zero matrix Paragraph
A−1 Inverse of a matrix Definition
T−1 Inverse of a transformation Definition
C[T]B The (B,C) -matrix of a linear transformation Definition
det(A) The determinant of a matrix Definition
AT Transpose of a matrix Definition
Aij Minor of a matrix Definition
Cij Cofactor of a matrix Definition
adj(A) Adjugate matrix Paragraph
vol(P) Volume of a region Theorem
vol(A) Volume of the parallelepiped of a matrix Theorem
T(S) The image of a region under a transformation Paragraph
Tr(A) Trace of a matrix Definition
Re(v) Real part of a complex vector Paragraph
Im(v) Imaginary part of a complex vector Paragraph
x·y Dot product of two vectors Definition
x⊥y x is orthogonal to y Paragraph
W⊥ Orthogonal complement of a subspace Definition
Row(A) Row space of a matrix Definition
xW Orthogonal projection of x onto W Definition
xW⊥ Orthogonal part of x with respect to W Definition
C The complex numbers Definition
z Complex conjugate Item
Re(z) Real part of a complex number Item
Im(z) Imaginary part of a complex number Item