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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
R n Real n -space Definition 1.1.1
A 12 B A vector Paragraph
0 The zero vector Paragraph
Span { v 1 , v 2 ,..., v k } Span of vectors Definition 1.2.9
{ x | condition } Set builder notation Note 1.2.10
R i Row i of a matrix Item
m × n matrix Size of a matrix Important Note 2.4.1
Col ( A ) Column space Definition 3.3.16
Nul ( A ) Null space Definition 3.3.16
dim V Dimension of a subspace Definition 3.4.3
rank ( A ) The rank of a matrix Definition 3.6.1
nullity ( A ) The nullity of a matrix Definition 3.6.1
T : R n R m transformation with domain R n and codomain R m Definition 4.1.17
Id R n Identity transformation Definition 4.1.20
e 1 , e 2 ,... Standard coordinate vectors Notation 4.3.11
I n n × n identity matrix Definition 4.3.13
a ij The i , j entry of a matrix Notation 4.4.16
0 The zero transformation Paragraph
0 The zero matrix Paragraph
A 1 Inverse of a matrix Definition 4.5.1
T 1 Inverse of a transformation Definition 4.5.14
det ( A ) The determinant of a matrix Definition 5.1.1
A T Transpose of a matrix Definition 5.1.23
A ij Minor of a matrix Definition 5.2.1
C ij Cofactor of a matrix Definition 5.2.1
adj ( A ) Adjugate matrix Paragraph
vol ( P ) Volume of a region Theorem 5.3.6
vol ( A ) Volume of the parallelepiped of a matrix Theorem 5.3.6
T ( S ) The image of a region under a transformation Paragraph
Tr ( A ) Trace of a matrix Definition 6.2.9
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 7.1.1
x y x is orthogonal to y Paragraph
W Orthogonal complement of a subspace Definition 7.2.1
Row ( A ) Row space of a matrix Definition 7.2.18
x W Orthogonal projection of x onto W Definition 7.3.3
x W Orthogonal part of x with respect to W Definition 7.3.3
C The complex numbers Definition A.0.28
z Complex conjugate Item
Re ( z ) Real part of a complex number Item
Im ( z ) Imaginary part of a complex number Item