WOLFRAM

Wolfram Language & System Documentation Center

ChessboardDistance[u,v]

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

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
See Also
Tech Notes
Related Guides
History
Cite this Page

ChessboardDistance

ChessboardDistance[u,v]

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

Details

  • Chessboard distance is effectively the maximum difference across all dimensions.
  • ChessboardDistance[u,v] is equivalent to Max[Abs[u-v]]. »

Examples

open all close all

Basic Examples  (2)

The chessboard distance between two vectors:

Chessboard distance between numeric vectors:

Scope  (2)

Compute the distance between any vectors of equal length:

Compute the distance between vectors of any precision:

Applications  (1)

Cluster data using chessboard distance:

Properties & Relations  (5)

Chessboard distance is the maximum of absolute differences:

Demonstrate the triangle inequality:

ChessboardDistance is equivalent to a Norm of a difference:

ChessboardDistance is less than or equal to ManhattanDistance:

ChessboardDistance is less than or equal to EuclideanDistance:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_chessboarddistance, author="Wolfram Research", title="{ChessboardDistance}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ChessboardDistance.html}", note=[Accessed: 08-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_chessboarddistance, organization={Wolfram Research}, title={ChessboardDistance}, year={2007}, url={https://reference.wolfram.com/language/ref/ChessboardDistance.html}, note=[Accessed: 08-August-2025]}