# Symbols:K

### 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}`

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### 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}`

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### 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`

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### 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`

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### 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`

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### Kilometre

- $\mathrm {km}$

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

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

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### Kilogram

- $\mathrm {kg}$

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

The $\LaTeX$ code for \(\mathrm {kg}\) is `\mathrm {kg}`

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