Symbols:I
Roman Numeral
- $\mathrm I$ or $\mathrm i$
The Roman numeral for $1$.
Its $\LaTeX$ code is \mathrm I or \mathrm i.
Imaginary Unit
- $i$
The entity $i := 0 + 1 i$ is known as the imaginary unit.
The $\LaTeX$ code for \(i\) is i .
Identity Element
- $i$ or $I$
Used (rarely) to denote the identity element of a group $\struct {G, \circ}$:
- $\forall x \in G: i \circ x = x = x \circ i$
The $\LaTeX$ code for \(i\) is i .
The $\LaTeX$ code for \(I\) is I .
Unit $x$ Vector
- $\mathbf i$
Used to denote the unit vector in the positive direction of the $x$-axis.
The $\LaTeX$ code for \(\mathbf i\) is \mathbf i .
Unit Quaternion
- $\mathbf i$
Used to denote one of the units in the system of quaternions.
The $\LaTeX$ code for \(\mathbf i\) is \mathbf i .
Identity Matrix
- $\mathbf I_n$
Used to denote the identity matrix whose order is $n$.
When the order is understood or not specified, the symbol $\mathbf I$ is used.
The $\LaTeX$ code for \(\mathbf I\) is \mathbf I .
Identity Mapping
- $I_S$
Used to denote the identity mapping on a set $S$:
- $\forall x \in S: \map {I_S} x = x$
When the set itself is understood, it is commonplace to leave out the subscript.
The $\LaTeX$ code for \(\map {I_S} x\) is \map {I_S} x .
Set of Integers
- $\Bbb I$
Rarely used instead of $\Z$ for the set of integers:
- $\Bbb I = \set {\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots}$.
Its $\LaTeX$ code is \Bbb I or \mathbb I or \Bbb Z.
Imaginary Part
- $\map \Im z$ or $\map {\operatorname {Im} } z$
The imaginary part of a complex number $z$.
The $\LaTeX$ code for \(\map \Im z\) is \map \Im z .
The $\LaTeX$ code for \(\map {\operatorname {Im} } z\) is \map {\operatorname {Im} } z .
Image (Relation Theory)
- $\operatorname {Img}$
Denotes the image of a relation or the image of a mapping.
The $\LaTeX$ code for \(\Img {\RR}\) is \Img {\RR} .
Interquartile Range
- $\operatorname {IQR}$
Let $Q_1$ and $Q_3$ be first and third quartiles.
The interquartile range is defined and denoted as:
- $\operatorname {IQR} := Q_3 - Q_1$
The $\LaTeX$ code for \(\operatorname {IQR}\) is \operatorname {IQR} .
Even Impulse Pair Function
- $\map {\operatorname {II} } x$
The even impulse pair function is the real function $\operatorname {II}: \R \to \R$ defined as:
- $\forall x \in \R: \map {\operatorname {II} } x := \dfrac 1 2 \map \delta {x + \dfrac 1 2} + \dfrac 1 2 \map \delta {x - \dfrac 1 2}$
where $\delta$ denotes the Dirac delta function.
The $\LaTeX$ code for \(\map {\operatorname {II} } x\) is \map {\operatorname {II} } x .
Odd Impulse Pair Function
- $\map {\operatorname {I_I} } x$
The odd impulse pair function is the real function $\operatorname {I_I}: \R \to \R$ defined as:
- $\forall x \in \R: \map {\operatorname {I_I} } x := \dfrac 1 2 \map \delta {x + \dfrac 1 2} - \dfrac 1 2 \map \delta {x - \dfrac 1 2}$
where $\delta$ denotes the Dirac delta function.
The $\LaTeX$ code for \(\map {\operatorname {I_I} } x\) is \map {\operatorname {I_I} } x .
Sampling Function
- $\map {\operatorname {III} } x$
The sampling function is the distribution $\operatorname {III}_T: \map \DD \R \to \R$ defined as:
- $\forall x \in \R: \map {\operatorname {III}_T } x := \ds \sum_{n \mathop \in \Z} \map \delta {x - T n}$
where:
- $T \in \R_{\ne 0}$ is a non-zero real number
- $\delta$ denotes the Dirac delta distribution.
When $T = 1$, it is usually omitted:
- $\forall x \in \R: \map {\operatorname {III} } x := \ds \sum_{n \mathop \in \Z} \map \delta {x - n}$
The $\LaTeX$ code for \(\map {\operatorname {III} } x\) is \map {\operatorname {III} } x .
Electric Current
- $I$
The usual symbol used to denote an electric current when only its scalar magnitude is being discussed is $I$.
Its $\LaTeX$ code is I .