Skip to main content


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 2.1.4
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 p } Span of vectors Definition 3.2.6
{ x | condition } Set builder notation Note 3.2.7
m × n matrix Dimensions of a matrix Important Note 3.3.1
Col ( A ) Column space Definition 3.6.17
Nul ( A ) Null space Definition 3.6.17
dim V Dimension of a subspace Definition 3.7.3
rank ( A ) The rank of a matrix Definition 3.9.1
nullity ( A ) The nullity of a matrix Definition 3.9.1
x A→ y image of a point under a transformation Definition 4.1.17
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
0 The zero transformation Paragraph
a ij The i , j entry of a matrix Notation 4.4.19
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 7.2.17
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