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 allBasic Examples (2)
Scope (2)
Applications (1)
Properties & Relations (5)
Chessboard distance is the maximum of absolute differences:
ChessboardDistance[{a, b, c}, {x, y, z}]Max[Abs[{a, b, c} - {x, y, z}]]Demonstrate the triangle inequality:
d1 = ChessboardDistance[{a, b}, {a, c}]d2 = ChessboardDistance[{a, c}, {d, c}]d3 = ChessboardDistance[{a, b}, {d, c}]Simplify[d3 <= d1 + d2]ChessboardDistance is equivalent to a Norm of a difference:
ChessboardDistance[{a, b, c}, {x, y, z}]Norm[{a, b, c} - {x, y, z}, Infinity]ChessboardDistance is less than or equal to ManhattanDistance:
u = {a, b, c};
v = {x, y, z};Simplify[ChessboardDistance[u, v] ≤ ManhattanDistance[u, v]]ChessboardDistance is less than or equal to EuclideanDistance:
u = {a, b, c};
v = {x, y, z};Simplify[ChessboardDistance[u, v] ≤ EuclideanDistance[u, v]]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