# Euclidean distance between two vectors (single row matrix)

I have two vectors (single row matrices). Assume that we already know the length len.

```A = [ x1 x2 x3 x4 x5 .... ]
B = [ y1 y2 y3 y4 y5 .... ]
```

To calculate Euclidean distance between them what is the fastest method. My first attempt is:

```diff = A - B
sum = 0
for column = 1:len
sum += diff(1, column)^2
distance = sqrt(sum)
```

I have loop through this methods millions of times. So, I am looking for something which is fast and correct. Note that I am not using MATLAB and don't have pdist2 API available.

```diff = A - B;
distance = sqrt(diff * diff');
```

or

```distance = norm(A - B);
```

```[val idx]    =  sort(sum(abs(Ti-Qi)./(1+Ti+Qi)));
```

or

```[val idx]    =  sort(sqrt(sum((Ti-Qi).^2)));
```

Val is the value and idx is the original index value of the column being sorted after applying Euclidean distance. (Matlab Code)

```diff = A - B;
distance = sqrt(sum(diff * diff')) % sum of squared diff
```

or

```distance = norm(A-B);
```