Euclidean distance of two matrices
First let's take a quick look at what your code is doing. Your innermost line of code is:

n[i]&lt;-sum(abs(a[i,]-b[j,])^2)


Due to how you've structured your for loops, this is run for times


with i=1 and j=1, setting n[1] to the squared distance between row 1 with a and row 1 of b,
with i=1 and j=2, overwriting n[1] to the squared distance between row 1 of a and row 2 of b,
with i=2 and j=1, setting n[2] to the squared distance between row 2 of a and row 1 of b, and
with i=2 and j=2, overwriting n[2] to the squared distance between row 2 of a and row 2 of b.


So we end up with n = c(34, 20), the squared distances between each row of a and the last row of b.

It seems most likely to me that you are trying to compute the distances between each pair of points (since your n is structured as a vector). In this case, check out what we accomplish with the following, much simpler code:

(a-b)^2
#      [,1] [,2]
# [1,]    4   16
# [2,]    4   16


The resulting matrix is the squared difference of each element in the two matrices. All we need to do is to sum up the rows:

n &lt;- rowSums((a-b)^2)
n
# [1] 20 20


Or if we wanted the actual distance instead of the squared distance:

n &lt;- sqrt(rowSums((a-b)^2))
n
# [1] 4.472136 4.472136


Note that we dramatically simplified the calculation; a nice side benefit is that this code is much faster than using a for loop in R.