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Wikipedia Description

The Minkowski distance is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance.The Minkowski distance of order p between two pointsis defined as:For, the Minkowski distance is a metric as a result of the Minkowski inequality. When, the distance between (0,0) and (1,1) is, but the point (0,1) is at a distance 1 from both of these points. Since this violates the triangle inequality, for it is not a metric.Minkowski distance is typically used with p being 1 or 2. The latter is the Euclidean distance, while the former is sometimes known as the Manhattan distance. In the limiting case of p reaching infinity, we obtain the Chebyshev distance:Similarly, for p reaching negative infinity, we have:The Minkowski distance can also be viewed as a multiple of the power mean of the component-wise differences between P and Q.

length, mathematics, minkowski