The Euclidean metric is the function d:R^n×R^n->R that assigns to any two vectors in Euclidean n-space x = (x_1, ..., x_n) and y = (y_1, ..., y_n) the number d(x, y) = sqrt((x_1 - y_1)^2 + ... + (x_n - y_n)^2), and so gives the "standard" distance between any two vectors in R^n.

distance | Euclidean space | Minkowski metric | vector norm