Notation
Contents
Notation#
This section summarizes major notation used in the book.
Numbers#
Notation |
Meaning |
Reference |
|---|---|---|
\(\Nat\) |
The set of natural numbers |
|
\(\ZZ\) |
The set of integers |
|
\(\QQ\) |
The set of rational numbers |
|
\(\RR\) |
The set of real numbers |
|
\(\ERL\) |
The extended real line \([-\infty, \infty]\) |
|
\(\CC\) |
The set of complex numbers |
|
\(\Re(x)\) |
The real part of a complex number |
|
\(\Im(x)\) |
The imaginary part of a complex number |
Sets and Functions#
Notation |
Meaning |
Reference |
|---|---|---|
\(\dom f\) |
Domain of a function \(f\) |
|
\(\range f\) |
Range of a function \(f\) |
|
\(\epi f\) |
Epigraph of a function \(f\) |
|
\(\supp f\) |
Support of a function \(f\) |
|
\(g \circ f\) |
Composition of functions \(g\) and \(f\) with \((g \circ f)(x) = g(f(x))\) |
Linear Algebra#
Notation |
Meaning |
|---|---|
\(\VV\) |
A vector space (usually finite dimensional) |
\(\EE\) |
A normed vector space (usually finite dimensional and Euclidean) |
\(\RR^n\) |
\(n\) dimensional Euclidean real vector space |
\(\RR^{m \times n}\) |
The space of \(m \times n\) real matrices |
\(\SS^{n}\) |
The space of \(n \times n\) symmetric real matrices |
\(\NullSpace(A)\) |
Null space of a matrix \(A\) |
\(\ColSpace(A)\) |
Column space of a matrix \(A\) |
\(\RowSpace(A)\) |
Row space of a matrix \(A\) |
\(\Range(A)\) |
Range of a set of vectors \(A\) |
\(\Nullity(A)\) |
Nullity of a an operator \(A\) |
\(\Trace(A)\) |
Trace of a matrix \(A\) |
\(\Diag(A)\) |
Diagonal of a matrix \(A\) |
\(\supp(v)\) |
Support of a vector \(v\) (non-zero indices) |
\(\bzero\) |
The all zeros vector |
\(\bone\) |
The all ones vector |
Topology / Metric Spaces#
Notation |
Meaning |
|---|---|
\(\interior A\) |
The interior of a set \(A\) |
\(\closure A\) |
The closure of a set \(A\) |
\(\boundary A\) |
The boundary of a set \(A\) |
\(\diam A\) |
The diam of a set \(A\) |
\(\relint A\) |
The relative interior of a set \(A\) |
Calculus#
Notation |
Meaning |
Reference |
|---|---|---|
\(\lim_{x \to a} f(x)\) |
Limit of \(f\) as \(x\) approaches \(a\) |
|
\(x \to a^-\) |
\(x\) approaches \(a\) from the left |
|
\(x \to a^+\) |
\(x\) approaches \(a\) from the right |
|
\(f(a^-)\) |
Left hand limit of \(f\) at \(x=a\) |
|
\(f(a^+)\) |
Right hand limit of \(f\) at \(x=a\) |
|
\(f'\) |
First derivative of \(f\) |
|
\(f^{(1)}\) |
1st derivative of \(f\) |
|
\(f^{(n)}\) |
n-th derivative of \(f\) |
|
\(f^{(0)}\) |
0-th derivative of \(f\) (\(f^{(0)}=f\)) |
|
\(f'_-(a)\) |
Left hand derivative of \(f\) at \(x=a\) |
|
\(f'_+(a)\) |
Right hand derivative of \(f\) at \(x=a\) |
|
\(\nabla f\) |
Gradient of \(f\) |
Convex Analysis#
Notation |
Meaning |
|---|---|
\(\prox_f\) |
The proximal operator for a function \(f\) |