Symbols:I

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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 .


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