mathvectordimensioneuclidean-distance

Calculate Euclidean distance between 4-dimensional vectors

Let's say I have two 4-dimensional vectors (i.e. a and b) as follows:

a = {a1, a2, a3, a4}
b= {b1, b2, b3, b4}

How do I compute the Euclidean distance between these vectors?

Solution

  • The euclidian distance calculus is independent of dimensions.

    In your case, the euclidian distance between a and b can be written as:

    d(a,b) = sqrt( sum_{ i=1 } ^ { 4 } (a[ i ] - b[ i ])^2 )

    Or, more specifically:

    d(a,b) = sqrt( (a1 - b1)^2 + (a2 - b2)^2 + (a3 -b3)^2 + (a4 - b4)^2 )