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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 1.1.4
R i Row i of a matrix Item
A 12 B A vector Paragraph
0 The zero vector Paragraph
Span { v 1 , v 2 ,..., v k } Span of vectors Definition 2.2.7
{ x | condition } Set builder notation Note 2.2.8
m × n matrix Size of a matrix Important Note 2.3.1
Col ( A ) Column space Definition 2.6.16
Nul ( A ) Null space Definition 2.6.16
dim V Dimension of a subspace Definition 2.7.3
rank ( A ) The rank of a matrix Definition 2.9.1
nullity ( A ) The nullity of a matrix Definition 2.9.1
T : R n R m transformation with domain R n and codomain R m Definition 3.1.17
Id R n Identity transformation Definition 3.1.20
e 1 , e 2 ,... Standard coordinate vectors Notation 3.3.11
I n n × n identity matrix Definition 3.3.13
a ij The i , j entry of a matrix Notation 3.4.16
0 The zero transformation Paragraph
0 The zero matrix Paragraph
A 1 Inverse of a matrix Definition 3.5.1
T 1 Inverse of a transformation Definition 3.5.14
det ( A ) The determinant of a matrix Definition 4.1.1
A T Transpose of a matrix Definition 4.1.23
A ij Minor of a matrix Definition 4.2.1
C ij Cofactor of a matrix Definition 4.2.1
adj ( A ) Adjugate matrix Paragraph
vol ( P ) Volume of a region Theorem 4.3.6
vol ( A ) Volume of the parallelepiped of a matrix Theorem 4.3.6
T ( S ) The image of a region under a transformation Paragraph
Tr ( A ) Trace of a matrix Definition 5.2.9
x · y Dot product of two vectors Definition 6.1.1
x y x is orthogonal to y Paragraph
W Orthogonal complement of a subspace Definition 6.2.1
Row ( A ) Row space of a matrix Definition 6.2.17
x W Orthogonal projection of x onto W Definition 6.3.3
x W Orthogonal part of x with respect to W Definition 6.3.3
C The complex numbers Definition A.0.26
z Complex conjugate Item
Re ( z ) Real part of a complex number Item
Im ( z ) Imaginary part of a complex number Item