the mathematical distance between two points, which is the sum of the absolute difference of their Cartesian coordinates

Manhattan Distance is the mathematical distance between two points, which is the sum of the absolute difference of their Cartesian coordinates.

the sum of absolute differences

Euclidean distances are root sum-of-squares of differences, and manhattan distances are the sum of absolute differences.

a distance metric between two points in a N dimensional vector space

Manhattan distance is a distance metric between two points in a N dimensional vector space.

a rectilinear distance

"Manhattan distance" is a rectilinear distance, named after the number of blocks north, south, east, or west a taxicab must travel on to reach a taxicab's destination on the grid of streets in parts of New York City.

the simple sum of the horizontal and vertical components or the distance between two points measured along axes at right angles

The Manhattan distance is the simple sum of the horizontal and vertical components or the distance between two points measured along axes at right angles.

The distance derived from this norm

The distance derived from this norm is called the Manhattan distance or ℓ 1 {\displaystyle \ell ^{1}} distance.

the shortest distance between two points on a grid

Manhattan distance is the shortest distance between two points on a grid.

the sum of absolute differences between points across all the dimensions

Manhattan Distance is the sum of absolute differences between points across all the dimensions.

the first root of the sum of differences raised to the first power, and

The Manhattan distance, or 1-norm, is the first root of the sum of differences raised to the first power, and the Euclidean distance, or 2-norm, is the square root of the sum of differences raised to the second power.

the sum of the x and y distances

This is really interesting, and in fact the sum of the x and y distances is called the Manhattan distance.

the first root of the sum of differences , and the Euclidean distance, or raised to the first power

The Manhattan distance, or 1-norm, is the first root of the sum of differences raised to the first power, and the Euclidean distance, or 2-norm, is the square root of the sum of differences raised to the second power.

the distance between a pair of vectors

The Manhattan distance (also known as L1 norm and Taxicab Distance) - calculates the distance between a pair of vectors, as if simulating a route for a Manhattan taxi driver driving from point A to point B - who is navigating the streets of Manhattan with the grid layout and one-way streets.

the rectilinear distance between two points: d = |x1 -

The Manhattan distance is the rectilinear distance between two points: d = |x1 -