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ChebyshevDistance[u,v]

gives the Chebyshev or sup norm distance between vectors u and v.

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Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
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ChebyshevDistance

As of Version 7.0, ChebyshevDistance is superseded by ChessboardDistance.

ChebyshevDistance[u,v]

gives the Chebyshev or sup norm distance between vectors u and v.

Details

  • ChebyshevDistance[u,v] is equivalent to Max[Abs[u-v]]. »

Examples

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Basic Examples  (2)

The Chebyshev distance between two vectors:

Chebyshev distance between numeric vectors:

Scope  (2)

Compute the distance between any vectors of equal length:

Compute the distance between vectors of any precision:

Applications  (2)

Cluster data using Chebyshev distance:

Demonstrate the triangle inequality:

Properties & Relations  (4)

Chebyshev distance is the maximum of absolute differences:

ChebyshevDistance is equivalent to a Norm of a difference:

ChebyshevDistance is less than or equal to ManhattanDistance:

ChebyshevDistance is less than or equal to EuclideanDistance:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_chebyshevdistance, author="Wolfram Research", title="{ChebyshevDistance}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ChebyshevDistance.html}", note=[Accessed: 28-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_chebyshevdistance, organization={Wolfram Research}, title={ChebyshevDistance}, year={2007}, url={https://reference.wolfram.com/language/ref/ChebyshevDistance.html}, note=[Accessed: 28-August-2025]}