# EuclideanDistance

EuclideanDistance[u,v]

gives the Euclidean distance between vectors u and v.

# Examples

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## Basic Examples(2)

Euclidean distance between two vectors:

Euclidean distance between numeric vectors:

## Scope(2)

Compute distance between any vectors of equal length:

Compute distance between vectors of any precision:

## Applications(2)

Cluster data using Euclidean distance:

Demonstrate the triangle inequality:

## Properties & Relations(7)

EuclideanDistance is equivalent to Norm of a difference:

The square of EuclideanDistance is SquaredEuclideanDistance:

EuclideanDistance is greater than or equal to ChessboardDistance:

CosineDistance includes a dot product scaled by Euclidean distances from the origin:

CorrelationDistance includes a dot product scaled by Euclidean distances from means:

StandardDeviation as a EuclideanDistance from the Mean:

EuclideanDistance computed from RootMeanSquare of a difference:

Wolfram Research (2007), EuclideanDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/EuclideanDistance.html.

#### Text

Wolfram Research (2007), EuclideanDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/EuclideanDistance.html.

#### CMS

Wolfram Language. 2007. "EuclideanDistance." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EuclideanDistance.html.

#### APA

Wolfram Language. (2007). EuclideanDistance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EuclideanDistance.html

#### BibTeX

@misc{reference.wolfram_2022_euclideandistance, author="Wolfram Research", title="{EuclideanDistance}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/EuclideanDistance.html}", note=[Accessed: 10-June-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_euclideandistance, organization={Wolfram Research}, title={EuclideanDistance}, year={2007}, url={https://reference.wolfram.com/language/ref/EuclideanDistance.html}, note=[Accessed: 10-June-2023 ]}