The k-Minkowski metric between two points $ P_1 = (x_1,x_2,...,x_n) $ and $ P_2 = (y_1,y_2,...,y_n) $ is defined as $ d_k = (\sum_{i=1}^n \parallel x_i-y_i \parallel ^k)^{\frac{1}{k}} $. Manhattan metric (k=1) and Euclidean metric(k=2) are the special cases of Minkowski metric. Here $ P_1 $ and $ P_2 $ are the points corresponding to feature vectors.

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett