# Symbols:K

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### kilo-

$\mathrm k$

The Système Internationale d'Unités symbol for the metric scaling prefix kilo, denoting $10^{\, 3 }$, is $\mathrm { k }$.

Its $\LaTeX$ code is \mathrm {k} .

### Subgroup

$K$

Frequently used, in conjunction with $H$, to represent a general subgroup of a given group $G$ when two such subgroups need to be discussed.

### Field

$K$

One of the letters used as a variable denoting a general field.

### Field as Algebraic Structure

$\struct {K, +, \circ}$

The full specification for a field, where $+$ and $\circ$ are respectively the addition and product operations.

The $\LaTeX$ code for $\struct {K, +, \circ}$ is \struct {K, +, \circ} .

### Unit Vector

$\mathbf k$

A unit vector, usually in the direction of the $z$-axis.

Hence it is usually aligned so as to be parallel to the vertical direction in a given frame of reference.

### Unit Quaternion

$\mathbf k$

Used to denote one of the units in the system of quaternions.

The $\LaTeX$ code for $\mathbf k$ is \mathbf k .

### Kelvin

$\mathrm K$

The symbol for the kelvin is $\mathrm K$.

Note that, unlike the symbols for other temperature scales, there is no degree symbol used here: ${}^\circ \mathrm K$ is technically incorrect.

Its $\LaTeX$ code is \mathrm K .

### Kernel

$K$

Often used to denote the kernel of a general homomorphism.

### Complete Elliptic Integral of the First Kind

$\map K k$

$\ds \map K k = \int \limits_0^{\pi / 2} \frac {\d \phi} {\sqrt {1 - k^2 \sin^2 \phi} }$

is the complete elliptic integral of the first kind, and is a function of $k$, defined on the interval $0 < k < 1$.

The $\LaTeX$ code for $\map K k$ is \map K k .

### Kilometre

$\mathrm {km}$

The symbol for the kilometre is $\mathrm {km}$:

$\mathrm k$ for kilo
$\mathrm m$ for metre.

Its $\LaTeX$ code is \mathrm {km} .

### Kilogram

$\mathrm {kg}$

The symbol for the kilogram is $\mathrm {kg}$.

The $\LaTeX$ code for $\mathrm {kg}$ is \mathrm {kg} .

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