Mathematical Foundations for Signal Processing, Communications, and Networking

Notations and Symbols

$\mathcal{A}$, $\mathcal{B}$, …	sets
{·}	set
$\mathcal{A}$\$\mathcal{B}$	set $\mathcal{A}$ without $\mathcal{B}$
∀	for all (propositional logic)
· Λ ·	AND operator (propositional logic)
∃	there exists (propositional logic)
∃!	there exists only one (propositional logic)
∣·∣	absolute value
i	$\sqrt{-1}$
≜	definition
ℝ, ℂ, ℤ, ℕ	real line, complex plane, set of all integers, set of natural numbers (including zero)
ℝn, ℂn	set of n-tuples with components in ℝ, ℂ
X	metric space X
$\mathcal{F}$	field $\mathcal{F}$
$\mathcal{V}$	vector space $\mathcal{V}$
dim ($\mathcal{V}$)	dimension of vector space $\mathcal{V}$
span($\mathcal{A}$)	linear span of set of vectors
a, b, …	vectors
A, B, …	matrices
aT, AT	transpose of the vector a and the matrix A
a*, a*, A*	complex conjugate of the scalar a, element-wise complex conjugate of the vector a, and the matrix ...