Minkowski distance

The Minkowski distance or Minkowski metric is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance. It is named after the German mathematician Hermann Minkowski. The Minkowski distance of order (where is an integer) between two points is defined as: For the Minkowski distance is a metric as a result of the Minkowski inequality. When the distance between and is but the point is at a distance from both of these points. Since this violates the triangle inequality, for it is not a metric. However, a metric can be obtained for these values by simply removing the exponent of The resulting metric is also an F-norm. Minkowski distance is typically used with being 1 or 2, which correspond to the Manhattan distance and the Euclidean distance, respectively.