Euclidean distance between two vectors of complex numbers

I have two vectors of complex numbers and want to compute Euclidean distance between them. whether I should use d = norm(A - B) or d = norm(abs(A) - abs(B))

Answer 1

[Matt J]

Suppose you have

>> A=1-i; B=1+i;

Which result do you consider correct,

 >> d = norm(A - B) , 

d =

       2
or

 >> d = norm(abs(A) - abs(B))

d =

       0

[Geetika]

shouldn't it be 0?

[Friedrich]

Take a piece of paper and a pen, draw a coordinate system and mark the points A and B in there. What do you think is the distance?

[Geetika]

See that way it is 2. Right. But actually I am calculating the feature vectors that are coming as complex numbers. So, if there are 2 similar objects , then the difference between feature vectors (complex numbers in my case) should give 0 and not 2. as the - sign in the conjugate would be because of the rotation. Isn't it so?

[Matt J]

What about when A=1, B=-1. Do you again want to consider their distance to be zero?

In any case, this is not a general question that anyone but you can know the answer to. This is driven by the needs of your specific application and so only you know what is right for that.

[dhruv jain]

Considering you are working on feature vectors which give complex numbers then you should consider euclidean distance