WOLFRAM

As of Version 7.0, ChebyshevDistance is superseded by ChessboardDistance.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)Summary of the most common use cases

The Chebyshev distance between two vectors:

Out[1]=1

Chebyshev distance between numeric vectors:

Out[1]=1

Scope  (2)Survey of the scope of standard use cases

Compute the distance between any vectors of equal length:

Out[1]=1

Compute the distance between vectors of any precision:

Out[1]=1

Applications  (2)Sample problems that can be solved with this function

Cluster data using Chebyshev distance:

Out[1]=1

Demonstrate the triangle inequality:

Out[1]=1
Out[2]=2
Out[3]=3
Out[4]=4

Properties & Relations  (4)Properties of the function, and connections to other functions

Chebyshev distance is the maximum of absolute differences:

Out[1]=1
Out[2]=2

ChebyshevDistance is equivalent to a Norm of a difference:

Out[1]=1
Out[2]=2

ChebyshevDistance is less than or equal to ManhattanDistance:

Out[2]=2

ChebyshevDistance is less than or equal to EuclideanDistance:

Out[2]=2
Wolfram Research (2007), ChebyshevDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/ChebyshevDistance.html.
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.

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.

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

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

BibTeX

@misc{reference.wolfram_2024_chebyshevdistance, author="Wolfram Research", title="{ChebyshevDistance}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ChebyshevDistance.html}", note=[Accessed: 09-January-2025 ]}

@misc{reference.wolfram_2024_chebyshevdistance, author="Wolfram Research", title="{ChebyshevDistance}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ChebyshevDistance.html}", note=[Accessed: 09-January-2025 ]}

BibLaTeX

@online{reference.wolfram_2024_chebyshevdistance, organization={Wolfram Research}, title={ChebyshevDistance}, year={2007}, url={https://reference.wolfram.com/language/ref/ChebyshevDistance.html}, note=[Accessed: 09-January-2025 ]}

@online{reference.wolfram_2024_chebyshevdistance, organization={Wolfram Research}, title={ChebyshevDistance}, year={2007}, url={https://reference.wolfram.com/language/ref/ChebyshevDistance.html}, note=[Accessed: 09-January-2025 ]}