7.2: B - Notation

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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 in Section 1.1
\(\mathbb{R}\)	The real numbers	Paragraph in Section 1.1
\(\mathbb{R}^n\)	Real \(n\)-space	Definition 1.1.4 in Section 1.1
\(R_i\)	Row \(i\) of a matrix	Item in Section 1.2
\(\left(\begin{array}{c}1\\2\end{array}\right)\)	A vector	Paragraph in Section 2.1
\(0\)	The zero vector	Paragraph in Section 2.1
\(\text{Span}\{v_1,\:v_2,\cdots ,v_k\}\)	Span of vectors	Definition 2.2.2 in Section 2.2
\(\{x\: | \: \text{condition}\}\)	Set builder notation	Note 2.2.3 in Section 2.2
\(m\times n\) matrix	Size of a matrix	Note 2.3.1 in Section 2.3
\(\text{Col}(A)\)	Column space	Definition 2.6.3 in Section 2.6
\(\text{Nul}(A)\)	Null space	Definition 2.6.3 in Section 2.6
\(\text{dim}V\)	Dimension of a subspace	Definition 2.7.2 in Section 2.7
\(\text{rank}(A)\)	The rank of a matrix	Definition 2.9.1 in Section 2.9
\(\text{nullity}(A)\)	The nullity of a matrix	Definition 2.9.1 in Section 2.9
\(T:\:\mathbb{R}^n\to\mathbb{R}^m\)	Transformation with the domain \(\mathbb{R}^n\) and codomain \(\mathbb{R}^m\)	Definition 3.1.1 in Section 3.1
\(\text{Id}_{\mathbb{R}^n}\)	Identity transformation	Definition 3.1.2 in Section 3.1
\(e_1,\:e_2,\cdots\)	Standard Coordinate Vectors	Note 3.3.2 in Section 3.3
\(I_n\)	\(n\times n\) identity matrix	Definition 3.3.2 in Section 3.3
\(a_{ij}\)	The \(i,\: j\) entry of a matrix	Definition 3.4.2 in Section 3.4
\(0\)	The zero transformation	Paragraph in Section 3.4
\(0\)	The zero matrix	Paragraph in Section 3.4
\(A^{-1}\)	Inverse of a matrix	Definition 3.5.1 in Section 3.5
\(T^{-1}\)	Inverse of a transformation	Definition 3.5.3 in Section 3.5
\(\det(A)\)	The determinant of a matrix	Definition 4.1.1 in Section 4.1
\(A^{T}\)	Transpose of a matrix	Definition 4.1.3 in Section 4.1
\(A_{ij}\)	Minor of a matrix	Definition 4.2.1 in Section 4.2
\(C_{ij}\)	Cofactor of a matrix	Definition 4.2.1 in Section 4.2
\(\text{adj}(A)\)	Adjugate matrix	Paragraph in Section 4.2
\(\text{vol}(P)\)	Volume of a region	Theorem 4.3.1 in Section 4.3
\(\text{vol}(A)\)	Volume of the parallelepiped of a matrix	Theorem 4.3.1 in Section 4.3
\(T(S)\)	The image of a region under a transformation	Paragraph in Section 4.3
\(\text{Tr}(A)\)	Trace of a matrix	Definition 5.2.2 in Section 5.2
\(\Re(v)\)	Real part of a complex vector	Paragraph in Section 5.5
\(\Im(v)\)	Imaginary part of a complex vector	Paragraph in Section 5.5
\(x\cdot y\)	Dot product of two vectors	Definition 6.1.1 in Section 6.1
\(x\perp y\)	\(x\) is orthogonal to \(y\)	Paragraph in Section 6.1
\(W^{\perp}\)	Orthogonal complement of a subspace	Definition 6.2.1 in Section 6.2
\(\text{Row}(A)\)	Row space of a matrix	Definition 6.2.2 in Section 6.2
\(x_{W}\)	Orthogonal projection of \(x\) onto \(W\)	Definition 6.3.2 in Section 6.3
\(x_{W^{\perp}}\)	Orthogonal part of \(x\) with respect to \(W\)	Definition 6.3.2 in Section 6.3
\(\mathbb{C}\)	The complex numbers	Definition 7.1.1 in Section 7.1
\(\overline{z}\)	Complex conjugate	Item in Section 7.1
\(\Re(z)\)	Real part of a complex number	Item in Section 7.1
\(\Im(z)\)	Imaginary part of a complex number	Item in Section 7.1