Definition:Euclidean Metric

Definition
Let $M_{1'} = \left({A_{1'}, d_{1'}}\right)$ and $M_{2'} = \left({A_{2'}, d_{2'}}\right)$ be metric spaces.

Let $A_{1'} \times A_{2'}$ be the cartesian product of $A_{1'}$ and $A_{2'}$.

The Euclidean metric on $A_{1'} \times A_{2'}$ is defined as:


 * $d_2 \left({x, y}\right) := \left({\left({d_{1'} \left({x_1, y_1}\right)}\right)^2 + \left({d_{2'} \left({x_2, y_2}\right)}\right)^2}\right)^{1/2}$

where $x = \left({x_1, x_2}\right), y = \left({y_1, y_2}\right) \in A_{1'} \times A_{2'}$.

Also see

 * Euclidean Metric is Metric

Also see

 * Definition:Product Metric